KILLED proof of input_Ri94Gu3qFe.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 11 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 0 ms] (14) typed CpxTrs (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (18) CdtProblem (19) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (20) CdtProblem (21) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxRelTRS (29) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (30) CpxTRS (31) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CpxWeightedTrs (33) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CpxWeightedTrs (35) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxTypedWeightedTrs (37) CompletionProof [UPPER BOUND(ID), 0 ms] (38) CpxTypedWeightedCompleteTrs (39) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CpxTypedWeightedCompleteTrs (41) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) InliningProof [UPPER BOUND(ID), 644 ms] (44) CpxRNTS (45) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxRNTS (47) CompletionProof [UPPER BOUND(ID), 0 ms] (48) CpxTypedWeightedCompleteTrs (49) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (194) CpxWeightedTrs (195) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CpxWeightedTrs (197) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CpxTypedWeightedTrs (199) CompletionProof [UPPER BOUND(ID), 0 ms] (200) CpxTypedWeightedCompleteTrs (201) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CpxTypedWeightedCompleteTrs (203) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms] (204) CpxRNTS (205) InliningProof [UPPER BOUND(ID), 316 ms] (206) CpxRNTS (207) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (208) CpxRNTS (209) CompletionProof [UPPER BOUND(ID), 0 ms] (210) CpxTypedWeightedCompleteTrs (211) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] (212) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) hd(cons(X, Y)) -> activate(X) tl(cons(X, Y)) -> activate(Y) 0 -> n__0 zeros -> n__zeros s(X) -> n__s(X) incr(X) -> n__incr(X) adx(X) -> n__adx(X) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(X)) -> s(X) activate(n__incr(X)) -> incr(activate(X)) activate(n__adx(X)) -> adx(activate(X)) activate(X) -> 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: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) hd(cons(X, Y)) -> activate(X) tl(cons(X, Y)) -> activate(Y) 0' -> n__0 zeros -> n__zeros s(X) -> n__s(X) incr(X) -> n__incr(X) adx(X) -> n__adx(X) activate(n__0) -> 0' activate(n__zeros) -> zeros activate(n__s(X)) -> s(X) activate(n__incr(X)) -> incr(activate(X)) activate(n__adx(X)) -> adx(activate(X)) activate(X) -> 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: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) hd(cons(X, Y)) -> activate(X) tl(cons(X, Y)) -> activate(Y) 0 -> n__0 zeros -> n__zeros s(X) -> n__s(X) incr(X) -> n__incr(X) adx(X) -> n__adx(X) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(X)) -> s(X) activate(n__incr(X)) -> incr(activate(X)) activate(n__adx(X)) -> adx(activate(X)) activate(X) -> X S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0 -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Tuples: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 S tuples: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 K tuples:none Defined Rule Symbols: nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1 Defined Pair Symbols: NATS, ZEROS, INCR_1, ADX_1, HD_1, TL_1, 0', S_1, ACTIVATE_1 Compound Symbols: c_2, c1, c2, c3_1, c4_1, c5, c6_2, c7_2, c8, c9_1, c10_1, c11, c12, c13_1, c14_1, c15_1, c16_2, c17_2, c18 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 The (relative) TRS S consists of the following rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0 -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 The (relative) TRS S consists of the following rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0' -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0' activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0' -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0' activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Types: NATS :: c c :: c6:c7:c8 -> c1:c2 -> c ADX :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c6:c7:c8 zeros :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr ZEROS :: c1:c2 c1 :: c1:c2 c2 :: c1:c2 INCR :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c3:c4:c5 cons :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c3 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5 ACTIVATE :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c13:c14:c15:c16:c17:c18 c4 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5 c5 :: c3:c4:c5 c6 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8 activate :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr n__adx :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c7 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8 c8 :: c6:c7:c8 HD :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c9 c9 :: c13:c14:c15:c16:c17:c18 -> c9 TL :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c10 c10 :: c13:c14:c15:c16:c17:c18 -> c10 0' :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c11 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr S :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c12 c12 :: c12 n__0 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c13 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c13:c14:c15:c16:c17:c18 n__zeros :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c14 :: c1:c2 -> c13:c14:c15:c16:c17:c18 n__s :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c15 :: c12 -> c13:c14:c15:c16:c17:c18 n__incr :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c16 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c13:c14:c15:c16:c17:c18 c17 :: c6:c7:c8 -> c13:c14:c15:c16:c17:c18 -> c13:c14:c15:c16:c17:c18 c18 :: c13:c14:c15:c16:c17:c18 nats :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr adx :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr incr :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr hd :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr tl :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr s :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr hole_c1_19 :: c hole_c6:c7:c82_19 :: c6:c7:c8 hole_c1:c23_19 :: c1:c2 hole_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr4_19 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr hole_c3:c4:c55_19 :: c3:c4:c5 hole_c13:c14:c15:c16:c17:c186_19 :: c13:c14:c15:c16:c17:c18 hole_c97_19 :: c9 hole_c108_19 :: c10 hole_c129_19 :: c12 gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19 :: Nat -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr gen_c13:c14:c15:c16:c17:c1811_19 :: Nat -> c13:c14:c15:c16:c17:c18 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: ADX, INCR, ACTIVATE, activate, adx, incr They will be analysed ascendingly in the following order: ADX = INCR ADX = ACTIVATE activate < ADX INCR = ACTIVATE activate < ACTIVATE activate = adx activate = incr adx = incr ---------------------------------------- (14) Obligation: Innermost TRS: Rules: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0' -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0' activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Types: NATS :: c c :: c6:c7:c8 -> c1:c2 -> c ADX :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c6:c7:c8 zeros :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr ZEROS :: c1:c2 c1 :: c1:c2 c2 :: c1:c2 INCR :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c3:c4:c5 cons :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c3 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5 ACTIVATE :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c13:c14:c15:c16:c17:c18 c4 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5 c5 :: c3:c4:c5 c6 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8 activate :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr n__adx :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c7 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8 c8 :: c6:c7:c8 HD :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c9 c9 :: c13:c14:c15:c16:c17:c18 -> c9 TL :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c10 c10 :: c13:c14:c15:c16:c17:c18 -> c10 0' :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c11 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr S :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c12 c12 :: c12 n__0 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c13 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> c13:c14:c15:c16:c17:c18 n__zeros :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c14 :: c1:c2 -> c13:c14:c15:c16:c17:c18 n__s :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c15 :: c12 -> c13:c14:c15:c16:c17:c18 n__incr :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr c16 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c13:c14:c15:c16:c17:c18 c17 :: c6:c7:c8 -> c13:c14:c15:c16:c17:c18 -> c13:c14:c15:c16:c17:c18 c18 :: c13:c14:c15:c16:c17:c18 nats :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr adx :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr incr :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr hd :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr tl :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr s :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr hole_c1_19 :: c hole_c6:c7:c82_19 :: c6:c7:c8 hole_c1:c23_19 :: c1:c2 hole_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr4_19 :: cons:n__adx:c11:n__0:n__zeros:n__s:n__incr hole_c3:c4:c55_19 :: c3:c4:c5 hole_c13:c14:c15:c16:c17:c186_19 :: c13:c14:c15:c16:c17:c18 hole_c97_19 :: c9 hole_c108_19 :: c10 hole_c129_19 :: c12 gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19 :: Nat -> cons:n__adx:c11:n__0:n__zeros:n__s:n__incr gen_c13:c14:c15:c16:c17:c1811_19 :: Nat -> c13:c14:c15:c16:c17:c18 Generator Equations: gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19(0) <=> n__0 gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19(+(x, 1)) <=> cons(n__0, gen_cons:n__adx:c11:n__0:n__zeros:n__s:n__incr10_19(x)) gen_c13:c14:c15:c16:c17:c1811_19(0) <=> c13(n__0) gen_c13:c14:c15:c16:c17:c1811_19(+(x, 1)) <=> c16(c3(c13(n__0)), gen_c13:c14:c15:c16:c17:c1811_19(x)) The following defined symbols remain to be analysed: incr, ADX, INCR, ACTIVATE, activate, adx They will be analysed ascendingly in the following order: ADX = INCR ADX = ACTIVATE activate < ADX INCR = ACTIVATE activate < ACTIVATE activate = adx activate = incr adx = incr ---------------------------------------- (15) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (16) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 The (relative) TRS S consists of the following rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0 -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (17) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (18) Obligation: Complexity Dependency Tuples Problem Rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0 -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Tuples: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 S tuples: NATS -> c(ADX(zeros), ZEROS) ZEROS -> c1 ZEROS -> c2 INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) INCR(z0) -> c5 ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ADX(z0) -> c8 HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) 0' -> c11 S(z0) -> c12 ACTIVATE(n__0) -> c13(0') ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ACTIVATE(z0) -> c18 K tuples:none Defined Rule Symbols: nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1 Defined Pair Symbols: NATS, ZEROS, INCR_1, ADX_1, HD_1, TL_1, 0', S_1, ACTIVATE_1 Compound Symbols: c_2, c1, c2, c3_1, c4_1, c5, c6_2, c7_2, c8, c9_1, c10_1, c11, c12, c13_1, c14_1, c15_1, c16_2, c17_2, c18 ---------------------------------------- (19) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) Removed 10 trailing nodes: ACTIVATE(n__zeros) -> c14(ZEROS) ACTIVATE(n__s(z0)) -> c15(S(z0)) ACTIVATE(n__0) -> c13(0') INCR(z0) -> c5 S(z0) -> c12 ACTIVATE(z0) -> c18 ZEROS -> c2 0' -> c11 ZEROS -> c1 ADX(z0) -> c8 ---------------------------------------- (20) Obligation: Complexity Dependency Tuples Problem Rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0 -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Tuples: NATS -> c(ADX(zeros), ZEROS) INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) S tuples: NATS -> c(ADX(zeros), ZEROS) INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1 Defined Pair Symbols: NATS, INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c_2, c3_1, c4_1, c6_2, c7_2, c16_2, c17_2 ---------------------------------------- (21) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (22) Obligation: Complexity Dependency Tuples Problem Rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0 -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) K tuples:none Defined Rule Symbols: nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1, NATS Compound Symbols: c3_1, c4_1, c6_2, c7_2, c16_2, c17_2, c_1 ---------------------------------------- (23) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: NATS -> c(ADX(zeros)) ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: nats -> adx(zeros) zeros -> cons(n__0, n__zeros) zeros -> n__zeros incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) 0 -> n__0 s(z0) -> n__s(z0) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1, NATS Compound Symbols: c3_1, c4_1, c6_2, c7_2, c16_2, c17_2, c_1 ---------------------------------------- (25) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: nats -> adx(zeros) hd(cons(z0, z1)) -> activate(z0) tl(cons(z0, z1)) -> activate(z1) ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1, NATS Compound Symbols: c3_1, c4_1, c6_2, c7_2, c16_2, c17_2, c_1 ---------------------------------------- (27) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (28) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) The (relative) TRS S consists of the following rules: NATS -> c(ADX(zeros)) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Rewrite Strategy: INNERMOST ---------------------------------------- (29) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (30) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (31) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (32) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1] ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) [1] NATS -> c(ADX(zeros)) [0] activate(n__0) -> 0 [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(activate(z0)) [0] activate(n__adx(z0)) -> adx(activate(z0)) [0] activate(z0) -> z0 [0] 0 -> n__0 [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [0] s(z0) -> n__s(z0) [0] incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0] incr(z0) -> n__incr(z0) [0] adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0] adx(z0) -> n__adx(z0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: 0 => 0' ---------------------------------------- (34) 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: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1] ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) [1] NATS -> c(ADX(zeros)) [0] activate(n__0) -> 0' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(activate(z0)) [0] activate(n__adx(z0)) -> adx(activate(z0)) [0] activate(z0) -> z0 [0] 0' -> n__0 [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [0] s(z0) -> n__s(z0) [0] incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0] incr(z0) -> n__incr(z0) [0] adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0] adx(z0) -> n__adx(z0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (35) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (36) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1] ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) [1] NATS -> c(ADX(zeros)) [0] activate(n__0) -> 0' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(activate(z0)) [0] activate(n__adx(z0)) -> adx(activate(z0)) [0] activate(z0) -> z0 [0] 0' -> n__0 [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [0] s(z0) -> n__s(z0) [0] incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0] incr(z0) -> n__incr(z0) [0] adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0] adx(z0) -> n__adx(z0) [0] The TRS has the following type information: INCR :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> c3:c4 cons :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s c3 :: c16:c17 -> c3:c4 ACTIVATE :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> c16:c17 c4 :: c16:c17 -> c3:c4 ADX :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> c6:c7 c6 :: c3:c4 -> c16:c17 -> c6:c7 activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s n__adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s c7 :: c3:c4 -> c16:c17 -> c6:c7 n__incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s c16 :: c3:c4 -> c16:c17 -> c16:c17 c17 :: c6:c7 -> c16:c17 -> c16:c17 NATS :: c c :: c6:c7 -> c zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s n__0 :: cons:n__adx:n__incr:n__0:n__zeros:n__s 0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s n__zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s n__s :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s s :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s -> cons:n__adx:n__incr:n__0:n__zeros:n__s Rewrite Strategy: INNERMOST ---------------------------------------- (37) 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: INCR_1 ADX_1 ACTIVATE_1 (c) The following functions are completely defined: NATS activate_1 0' zeros s_1 incr_1 adx_1 Due to the following rules being added: NATS -> const3 [0] activate(v0) -> null_activate [0] 0' -> null_0' [0] zeros -> null_zeros [0] s(v0) -> null_s [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] And the following fresh constants: const3, null_activate, null_0', null_zeros, null_s, null_incr, null_adx, const, const1, const2 ---------------------------------------- (38) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1] ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) [1] NATS -> c(ADX(zeros)) [0] activate(n__0) -> 0' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(activate(z0)) [0] activate(n__adx(z0)) -> adx(activate(z0)) [0] activate(z0) -> z0 [0] 0' -> n__0 [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [0] s(z0) -> n__s(z0) [0] incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0] incr(z0) -> n__incr(z0) [0] adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0] adx(z0) -> n__adx(z0) [0] NATS -> const3 [0] activate(v0) -> null_activate [0] 0' -> null_0' [0] zeros -> null_zeros [0] s(v0) -> null_s [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] The TRS has the following type information: INCR :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c3:c4 cons :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c3 :: c16:c17 -> c3:c4 ACTIVATE :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c16:c17 c4 :: c16:c17 -> c3:c4 ADX :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c6:c7 c6 :: c3:c4 -> c16:c17 -> c6:c7 activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c7 :: c3:c4 -> c16:c17 -> c6:c7 n__incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c16 :: c3:c4 -> c16:c17 -> c16:c17 c17 :: c6:c7 -> c16:c17 -> c16:c17 NATS :: c:const3 c :: c6:c7 -> c:const3 zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__0 :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx 0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx const3 :: c:const3 null_activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx const :: c3:c4 const1 :: c16:c17 const2 :: c6:c7 Rewrite Strategy: INNERMOST ---------------------------------------- (39) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (40) 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: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1] ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1] ACTIVATE(n__incr(n__0)) -> c16(INCR(0'), ACTIVATE(n__0)) [1] ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros), ACTIVATE(n__zeros)) [1] ACTIVATE(n__incr(n__s(z047))) -> c16(INCR(s(z047)), ACTIVATE(n__s(z047))) [1] ACTIVATE(n__incr(n__incr(z048))) -> c16(INCR(incr(activate(z048))), ACTIVATE(n__incr(z048))) [1] ACTIVATE(n__incr(n__adx(z049))) -> c16(INCR(adx(activate(z049))), ACTIVATE(n__adx(z049))) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(null_activate), ACTIVATE(z0)) [1] ACTIVATE(n__adx(n__0)) -> c17(ADX(0'), ACTIVATE(n__0)) [1] ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros), ACTIVATE(n__zeros)) [1] ACTIVATE(n__adx(n__s(z050))) -> c17(ADX(s(z050)), ACTIVATE(n__s(z050))) [1] ACTIVATE(n__adx(n__incr(z051))) -> c17(ADX(incr(activate(z051))), ACTIVATE(n__incr(z051))) [1] ACTIVATE(n__adx(n__adx(z052))) -> c17(ADX(adx(activate(z052))), ACTIVATE(n__adx(z052))) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(null_activate), ACTIVATE(z0)) [1] NATS -> c(ADX(cons(n__0, n__zeros))) [0] NATS -> c(ADX(n__zeros)) [0] NATS -> c(ADX(null_zeros)) [0] activate(n__0) -> 0' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(n__0)) -> incr(0') [0] activate(n__incr(n__zeros)) -> incr(zeros) [0] activate(n__incr(n__s(z053))) -> incr(s(z053)) [0] activate(n__incr(n__incr(z054))) -> incr(incr(activate(z054))) [0] activate(n__incr(n__adx(z055))) -> incr(adx(activate(z055))) [0] activate(n__incr(z0)) -> incr(z0) [0] activate(n__incr(z0)) -> incr(null_activate) [0] activate(n__adx(n__0)) -> adx(0') [0] activate(n__adx(n__zeros)) -> adx(zeros) [0] activate(n__adx(n__s(z056))) -> adx(s(z056)) [0] activate(n__adx(n__incr(z057))) -> adx(incr(activate(z057))) [0] activate(n__adx(n__adx(z058))) -> adx(adx(activate(z058))) [0] activate(n__adx(z0)) -> adx(z0) [0] activate(n__adx(z0)) -> adx(null_activate) [0] activate(z0) -> z0 [0] 0' -> n__0 [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [0] s(z0) -> n__s(z0) [0] incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0] incr(z0) -> n__incr(z0) [0] adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0] adx(z0) -> n__adx(z0) [0] NATS -> const3 [0] activate(v0) -> null_activate [0] 0' -> null_0' [0] zeros -> null_zeros [0] s(v0) -> null_s [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] The TRS has the following type information: INCR :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c3:c4 cons :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c3 :: c16:c17 -> c3:c4 ACTIVATE :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c16:c17 c4 :: c16:c17 -> c3:c4 ADX :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c6:c7 c6 :: c3:c4 -> c16:c17 -> c6:c7 activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c7 :: c3:c4 -> c16:c17 -> c6:c7 n__incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c16 :: c3:c4 -> c16:c17 -> c16:c17 c17 :: c6:c7 -> c16:c17 -> c16:c17 NATS :: c:const3 c :: c6:c7 -> c:const3 zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__0 :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx 0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx const3 :: c:const3 null_activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx const :: c3:c4 const1 :: c16:c17 const2 :: c6:c7 Rewrite Strategy: INNERMOST ---------------------------------------- (41) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: n__0 => 0 n__zeros => 1 const3 => 0 null_activate => 0 null_0' => 0 null_zeros => 0 null_s => 0 null_incr => 0 null_adx => 0 const => 0 const1 => 0 const2 => 0 ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 0 }-> 0 :|: ACTIVATE(z) -{ 1 }-> 1 + INCR(z0) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(zeros) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + INCR(s(z047)) + ACTIVATE(1 + z047) :|: z = 1 + (1 + z047), z047 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(incr(activate(z048))) + ACTIVATE(1 + z048) :|: z048 >= 0, z = 1 + (1 + z048) ACTIVATE(z) -{ 1 }-> 1 + INCR(adx(activate(z049))) + ACTIVATE(1 + z049) :|: z = 1 + (1 + z049), z049 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(0') + ACTIVATE(0) :|: z = 1 + 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(z0) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(zeros) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + ADX(s(z050)) + ACTIVATE(1 + z050) :|: z = 1 + (1 + z050), z050 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(incr(activate(z051))) + ACTIVATE(1 + z051) :|: z = 1 + (1 + z051), z051 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(adx(activate(z052))) + ACTIVATE(1 + z052) :|: z052 >= 0, z = 1 + (1 + z052) ACTIVATE(z) -{ 1 }-> 1 + ADX(0') + ACTIVATE(0) :|: z = 1 + 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 NATS -{ 0 }-> 0 :|: NATS -{ 0 }-> 1 + ADX(1) :|: NATS -{ 0 }-> 1 + ADX(0) :|: NATS -{ 0 }-> 1 + ADX(1 + 0 + 1) :|: activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> zeros :|: z = 1 activate(z) -{ 0 }-> s(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> incr(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> incr(zeros) :|: z = 1 + 1 activate(z) -{ 0 }-> incr(s(z053)) :|: z053 >= 0, z = 1 + (1 + z053) activate(z) -{ 0 }-> incr(incr(activate(z054))) :|: z054 >= 0, z = 1 + (1 + z054) activate(z) -{ 0 }-> incr(adx(activate(z055))) :|: z = 1 + (1 + z055), z055 >= 0 activate(z) -{ 0 }-> incr(0') :|: z = 1 + 0 activate(z) -{ 0 }-> incr(0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> adx(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> adx(zeros) :|: z = 1 + 1 activate(z) -{ 0 }-> adx(s(z056)) :|: z056 >= 0, z = 1 + (1 + z056) activate(z) -{ 0 }-> adx(incr(activate(z057))) :|: z = 1 + (1 + z057), z057 >= 0 activate(z) -{ 0 }-> adx(adx(activate(z058))) :|: z = 1 + (1 + z058), z058 >= 0 activate(z) -{ 0 }-> adx(0') :|: z = 1 + 0 activate(z) -{ 0 }-> adx(0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> 0' :|: z = 0 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 adx(z) -{ 0 }-> incr(1 + activate(z0) + (1 + activate(z1))) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 incr(z) -{ 0 }-> 1 + (1 + activate(z0)) + (1 + activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 zeros -{ 0 }-> 1 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: ---------------------------------------- (43) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: 0' -{ 0 }-> 0 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: zeros -{ 0 }-> 1 :|: s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 0 }-> 0 :|: ACTIVATE(z) -{ 1 }-> 1 + INCR(z0) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(incr(activate(z048))) + ACTIVATE(1 + z048) :|: z048 >= 0, z = 1 + (1 + z048) ACTIVATE(z) -{ 1 }-> 1 + INCR(adx(activate(z049))) + ACTIVATE(1 + z049) :|: z = 1 + (1 + z049), z049 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(1) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(0) :|: z = 1 + 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(1 + z047) :|: z = 1 + (1 + z047), z047 >= 0, v0 >= 0, z047 = v0 ACTIVATE(z) -{ 1 }-> 1 + INCR(1 + z0) + ACTIVATE(1 + z047) :|: z = 1 + (1 + z047), z047 >= 0, z047 = z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(1 + 0 + 1) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + ADX(z0) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(incr(activate(z051))) + ACTIVATE(1 + z051) :|: z = 1 + (1 + z051), z051 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(adx(activate(z052))) + ACTIVATE(1 + z052) :|: z052 >= 0, z = 1 + (1 + z052) ACTIVATE(z) -{ 1 }-> 1 + ADX(1) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(0) :|: z = 1 + 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(1 + z050) :|: z = 1 + (1 + z050), z050 >= 0, v0 >= 0, z050 = v0 ACTIVATE(z) -{ 1 }-> 1 + ADX(1 + z0) + ACTIVATE(1 + z050) :|: z = 1 + (1 + z050), z050 >= 0, z050 = z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(1 + 0 + 1) + ACTIVATE(1) :|: z = 1 + 1 ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 NATS -{ 0 }-> 0 :|: NATS -{ 0 }-> 1 + ADX(1) :|: NATS -{ 0 }-> 1 + ADX(0) :|: NATS -{ 0 }-> 1 + ADX(1 + 0 + 1) :|: activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> incr(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> incr(incr(activate(z054))) :|: z054 >= 0, z = 1 + (1 + z054) activate(z) -{ 0 }-> incr(adx(activate(z055))) :|: z = 1 + (1 + z055), z055 >= 0 activate(z) -{ 0 }-> incr(1) :|: z = 1 + 1 activate(z) -{ 0 }-> incr(0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> incr(0) :|: z = 1 + 0 activate(z) -{ 0 }-> incr(0) :|: z = 1 + 1 activate(z) -{ 0 }-> incr(0) :|: z053 >= 0, z = 1 + (1 + z053), v0 >= 0, z053 = v0 activate(z) -{ 0 }-> incr(1 + z0) :|: z053 >= 0, z = 1 + (1 + z053), z053 = z0, z0 >= 0 activate(z) -{ 0 }-> incr(1 + 0 + 1) :|: z = 1 + 1 activate(z) -{ 0 }-> adx(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> adx(incr(activate(z057))) :|: z = 1 + (1 + z057), z057 >= 0 activate(z) -{ 0 }-> adx(adx(activate(z058))) :|: z = 1 + (1 + z058), z058 >= 0 activate(z) -{ 0 }-> adx(1) :|: z = 1 + 1 activate(z) -{ 0 }-> adx(0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> adx(0) :|: z = 1 + 0 activate(z) -{ 0 }-> adx(0) :|: z = 1 + 1 activate(z) -{ 0 }-> adx(0) :|: z056 >= 0, z = 1 + (1 + z056), v0 >= 0, z056 = v0 activate(z) -{ 0 }-> adx(1 + z0) :|: z056 >= 0, z = 1 + (1 + z056), z056 = z0, z0 >= 0 activate(z) -{ 0 }-> adx(1 + 0 + 1) :|: z = 1 + 1 activate(z) -{ 0 }-> 1 :|: z = 1 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 activate(z) -{ 0 }-> 0 :|: z = 0 activate(z) -{ 0 }-> 0 :|: z = 1 activate(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, z0 = v0 activate(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0 activate(z) -{ 0 }-> 1 + 0 + 1 :|: z = 1 adx(z) -{ 0 }-> incr(1 + activate(z0) + (1 + activate(z1))) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 incr(z) -{ 0 }-> 1 + (1 + activate(z0)) + (1 + activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 zeros -{ 0 }-> 1 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: ---------------------------------------- (45) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 0 }-> 0 :|: ACTIVATE(z) -{ 1 }-> 1 + INCR(incr(activate(z - 2))) + ACTIVATE(1 + (z - 2)) :|: z - 2 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(adx(activate(z - 2))) + ACTIVATE(1 + (z - 2)) :|: z - 2 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(1) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(0) :|: z = 1 + 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(z - 1) :|: z - 1 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(0) + ACTIVATE(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, z - 2 = v0 ACTIVATE(z) -{ 1 }-> 1 + INCR(z - 1) + ACTIVATE(z - 1) :|: z - 1 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(1 + z0) + ACTIVATE(1 + (z - 2)) :|: z - 2 >= 0, z - 2 = z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(1 + 0 + 1) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + ADX(incr(activate(z - 2))) + ACTIVATE(1 + (z - 2)) :|: z - 2 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(adx(activate(z - 2))) + ACTIVATE(1 + (z - 2)) :|: z - 2 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(1) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(1) :|: z = 1 + 1 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(0) :|: z = 1 + 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(z - 1) :|: z - 1 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(0) + ACTIVATE(1 + (z - 2)) :|: z - 2 >= 0, v0 >= 0, z - 2 = v0 ACTIVATE(z) -{ 1 }-> 1 + ADX(z - 1) + ACTIVATE(z - 1) :|: z - 1 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(1 + z0) + ACTIVATE(1 + (z - 2)) :|: z - 2 >= 0, z - 2 = z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(1 + 0 + 1) + ACTIVATE(1) :|: z = 1 + 1 ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 NATS -{ 0 }-> 0 :|: NATS -{ 0 }-> 1 + ADX(1) :|: NATS -{ 0 }-> 1 + ADX(0) :|: NATS -{ 0 }-> 1 + ADX(1 + 0 + 1) :|: activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> incr(incr(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 0 }-> incr(adx(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 0 }-> incr(1) :|: z = 1 + 1 activate(z) -{ 0 }-> incr(0) :|: z - 1 >= 0 activate(z) -{ 0 }-> incr(0) :|: z = 1 + 0 activate(z) -{ 0 }-> incr(0) :|: z = 1 + 1 activate(z) -{ 0 }-> incr(0) :|: z - 2 >= 0, v0 >= 0, z - 2 = v0 activate(z) -{ 0 }-> incr(z - 1) :|: z - 1 >= 0 activate(z) -{ 0 }-> incr(1 + z0) :|: z - 2 >= 0, z - 2 = z0, z0 >= 0 activate(z) -{ 0 }-> incr(1 + 0 + 1) :|: z = 1 + 1 activate(z) -{ 0 }-> adx(incr(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 0 }-> adx(adx(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 0 }-> adx(1) :|: z = 1 + 1 activate(z) -{ 0 }-> adx(0) :|: z - 1 >= 0 activate(z) -{ 0 }-> adx(0) :|: z = 1 + 0 activate(z) -{ 0 }-> adx(0) :|: z = 1 + 1 activate(z) -{ 0 }-> adx(0) :|: z - 2 >= 0, v0 >= 0, z - 2 = v0 activate(z) -{ 0 }-> adx(z - 1) :|: z - 1 >= 0 activate(z) -{ 0 }-> adx(1 + z0) :|: z - 2 >= 0, z - 2 = z0, z0 >= 0 activate(z) -{ 0 }-> adx(1 + 0 + 1) :|: z = 1 + 1 activate(z) -{ 0 }-> 1 :|: z = 1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z = 0 activate(z) -{ 0 }-> 0 :|: z = 1 activate(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, z - 1 = v0 activate(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, z - 1 = z0', z0' >= 0 activate(z) -{ 0 }-> 1 + 0 + 1 :|: z = 1 adx(z) -{ 0 }-> incr(1 + activate(z0) + (1 + activate(z1))) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 adx(z) -{ 0 }-> 0 :|: z >= 0 adx(z) -{ 0 }-> 1 + z :|: z >= 0 incr(z) -{ 0 }-> 0 :|: z >= 0 incr(z) -{ 0 }-> 1 + z :|: z >= 0 incr(z) -{ 0 }-> 1 + (1 + activate(z0)) + (1 + activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 s(z) -{ 0 }-> 0 :|: z >= 0 s(z) -{ 0 }-> 1 + z :|: z >= 0 zeros -{ 0 }-> 1 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: ---------------------------------------- (47) 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: NATS -> null_NATS [0] activate(v0) -> null_activate [0] 0' -> null_0' [0] zeros -> null_zeros [0] s(v0) -> null_s [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] INCR(v0) -> null_INCR [0] ADX(v0) -> null_ADX [0] ACTIVATE(v0) -> null_ACTIVATE [0] And the following fresh constants: null_NATS, null_activate, null_0', null_zeros, null_s, null_incr, null_adx, null_INCR, null_ADX, null_ACTIVATE ---------------------------------------- (48) 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: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) [1] ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) [1] NATS -> c(ADX(zeros)) [0] activate(n__0) -> 0' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(activate(z0)) [0] activate(n__adx(z0)) -> adx(activate(z0)) [0] activate(z0) -> z0 [0] 0' -> n__0 [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [0] s(z0) -> n__s(z0) [0] incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) [0] incr(z0) -> n__incr(z0) [0] adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) [0] adx(z0) -> n__adx(z0) [0] NATS -> null_NATS [0] activate(v0) -> null_activate [0] 0' -> null_0' [0] zeros -> null_zeros [0] s(v0) -> null_s [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] INCR(v0) -> null_INCR [0] ADX(v0) -> null_ADX [0] ACTIVATE(v0) -> null_ACTIVATE [0] The TRS has the following type information: INCR :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c3:c4:null_INCR cons :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c3 :: c16:c17:null_ACTIVATE -> c3:c4:null_INCR ACTIVATE :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c16:c17:null_ACTIVATE c4 :: c16:c17:null_ACTIVATE -> c3:c4:null_INCR ADX :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> c6:c7:null_ADX c6 :: c3:c4:null_INCR -> c16:c17:null_ACTIVATE -> c6:c7:null_ADX activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c7 :: c3:c4:null_INCR -> c16:c17:null_ACTIVATE -> c6:c7:null_ADX n__incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx c16 :: c3:c4:null_INCR -> c16:c17:null_ACTIVATE -> c16:c17:null_ACTIVATE c17 :: c6:c7:null_ADX -> c16:c17:null_ACTIVATE -> c16:c17:null_ACTIVATE NATS :: c:null_NATS c :: c6:c7:null_ADX -> c:null_NATS zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__0 :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx 0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx n__s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx -> cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_NATS :: c:null_NATS null_activate :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_0' :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_zeros :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_s :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_incr :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_adx :: cons:n__adx:n__incr:n__0:n__zeros:n__s:null_activate:null_0':null_zeros:null_s:null_incr:null_adx null_INCR :: c3:c4:null_INCR null_ADX :: c6:c7:null_ADX null_ACTIVATE :: c16:c17:null_ACTIVATE Rewrite Strategy: INNERMOST ---------------------------------------- (49) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: n__0 => 0 n__zeros => 1 null_NATS => 0 null_activate => 0 null_0' => 0 null_zeros => 0 null_s => 0 null_incr => 0 null_adx => 0 null_INCR => 0 null_ADX => 0 null_ACTIVATE => 0 ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 0 }-> 0 :|: ACTIVATE(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ACTIVATE(z) -{ 1 }-> 1 + INCR(activate(z0)) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(activate(z0)) + ACTIVATE(z0) :|: z = 1 + z0, z0 >= 0 ADX(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ADX(z) -{ 1 }-> 1 + INCR(1 + activate(z0) + (1 + activate(z1))) + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 INCR(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 NATS -{ 0 }-> 0 :|: NATS -{ 0 }-> 1 + ADX(zeros) :|: activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> zeros :|: z = 1 activate(z) -{ 0 }-> s(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> incr(activate(z0)) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> adx(activate(z0)) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> 0' :|: z = 0 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 adx(z) -{ 0 }-> incr(1 + activate(z0) + (1 + activate(z1))) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 adx(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 adx(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 incr(z) -{ 0 }-> 1 + (1 + activate(z0)) + (1 + activate(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 zeros -{ 0 }-> 1 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(z0, z1)) -> c6(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z0)) by ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(n__0)) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(n__0)) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(n__0)) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1, NATS Compound Symbols: c3_1, c4_1, c7_2, c16_2, c17_2, c_1, c6_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1, NATS Compound Symbols: c3_1, c4_1, c7_2, c16_2, c17_2, c_1, c6_2, c6_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(z0, z1)) -> c7(INCR(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE(z1)) by ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(n__0)) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(n__0)) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(n__0)) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, NATS, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c_1, c6_2, c6_1, c7_2 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, NATS, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__incr(z0)) -> c16(INCR(activate(z0)), ACTIVATE(z0)) by ACTIVATE(n__incr(n__0)) -> c16(INCR(0), ACTIVATE(n__0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros), ACTIVATE(n__zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0)), ACTIVATE(n__s(z0))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__0)) -> c16(INCR(0), ACTIVATE(n__0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros), ACTIVATE(n__zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0)), ACTIVATE(n__s(z0))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__0)) -> c16(INCR(0), ACTIVATE(n__0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros), ACTIVATE(n__zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0)), ACTIVATE(n__s(z0))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, NATS, ADX_1 Compound Symbols: c3_1, c4_1, c17_2, c_1, c6_2, c6_1, c7_2, c7_1, c16_2 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) NATS -> c(ADX(zeros)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, NATS, ADX_1 Compound Symbols: c3_1, c4_1, c17_2, c_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__adx(z0)) -> c17(ADX(activate(z0)), ACTIVATE(z0)) by ACTIVATE(n__adx(n__0)) -> c17(ADX(0), ACTIVATE(n__0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros), ACTIVATE(n__zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0)), ACTIVATE(n__s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) NATS -> c(ADX(zeros)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__0)) -> c17(ADX(0), ACTIVATE(n__0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros), ACTIVATE(n__zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0)), ACTIVATE(n__s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__0)) -> c17(ADX(0), ACTIVATE(n__0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros), ACTIVATE(n__zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0)), ACTIVATE(n__s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, NATS, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) NATS -> c(ADX(zeros)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, NATS, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace NATS -> c(ADX(zeros)) by NATS -> c(ADX(cons(n__0, n__zeros))) NATS -> c(ADX(n__zeros)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) NATS -> c(ADX(cons(n__0, n__zeros))) NATS -> c(ADX(n__zeros)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) K tuples: NATS -> c(ADX(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1, NATS Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c_1 ---------------------------------------- (69) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: NATS -> c(ADX(cons(n__0, n__zeros))) Removed 1 trailing nodes: NATS -> c(ADX(n__zeros)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(0))), ACTIVATE(x0)) by ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(zeros))), ACTIVATE(x0)) by ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(s(z0)))), ACTIVATE(x0)) by ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1)))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1)))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(x0)) by ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(x0)) by ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, z0)) -> c6(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(x0)) by ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))), ACTIVATE(n__0)) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))), ACTIVATE(n__0)) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1))), ACTIVATE(n__0)) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1))), ACTIVATE(n__zeros)) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) by ADX(cons(n__incr(x0), n__0)) -> c6(INCR(cons(incr(activate(x0)), n__adx(0))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(x0), n__zeros)) -> c6(INCR(cons(incr(activate(x0)), n__adx(zeros))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(x0), n__s(z0))) -> c6(INCR(cons(incr(activate(x0)), n__adx(s(z0)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(x0), n__incr(z0))) -> c6(INCR(cons(incr(activate(x0)), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(x0), n__adx(z0))) -> c6(INCR(cons(incr(activate(x0)), n__adx(adx(activate(z0))))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(x0), z0)) -> c6(INCR(cons(incr(activate(x0)), n__adx(z0))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) by ADX(cons(n__adx(x0), n__0)) -> c6(INCR(cons(adx(activate(x0)), n__adx(0))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(x0), n__zeros)) -> c6(INCR(cons(adx(activate(x0)), n__adx(zeros))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(x0), n__s(z0))) -> c6(INCR(cons(adx(activate(x0)), n__adx(s(z0)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(x0), n__incr(z0))) -> c6(INCR(cons(adx(activate(x0)), n__adx(incr(activate(z0))))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(x0), n__adx(z0))) -> c6(INCR(cons(adx(activate(x0)), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(x0), z0)) -> c6(INCR(cons(adx(activate(x0)), n__adx(z0))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(z0)) by ADX(cons(x0, n__0)) -> c6(INCR(cons(x0, n__adx(0))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(x0, n__adx(zeros))), ACTIVATE(x0)) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(x0, n__adx(s(z0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(x0, n__adx(incr(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(x0, n__adx(adx(activate(z0))))), ACTIVATE(x0)) ADX(cons(x0, z0)) -> c6(INCR(cons(x0, n__adx(z0))), ACTIVATE(x0)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(activate(x1))))) by ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c6(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__0, n__incr(z0))) -> c6(INCR(cons(0, n__adx(incr(activate(z0)))))) ADX(cons(n__0, n__adx(z0))) -> c6(INCR(cons(0, n__adx(adx(activate(z0)))))) ADX(cons(n__0, z0)) -> c6(INCR(cons(0, n__adx(z0)))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(activate(x1))))) by ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c6(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__zeros, n__incr(z0))) -> c6(INCR(cons(zeros, n__adx(incr(activate(z0)))))) ADX(cons(n__zeros, n__adx(z0))) -> c6(INCR(cons(zeros, n__adx(adx(activate(z0)))))) ADX(cons(n__zeros, z0)) -> c6(INCR(cons(zeros, n__adx(z0)))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c6_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(activate(x1))))) by ADX(cons(n__s(x0), n__0)) -> c6(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c6(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c6(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__s(x0), n__incr(z0))) -> c6(INCR(cons(s(x0), n__adx(incr(activate(z0)))))) ADX(cons(n__s(x0), n__adx(z0))) -> c6(INCR(cons(s(x0), n__adx(adx(activate(z0)))))) ADX(cons(n__s(x0), z0)) -> c6(INCR(cons(s(x0), n__adx(z0)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) by ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) by ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, z0)) -> c7(INCR(cons(activate(x0), n__adx(z0))), ACTIVATE(z0)) by ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(activate(x1)))), ACTIVATE(x1)) by ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__0, n__incr(z0))) -> c7(INCR(cons(0, n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__adx(z0))) -> c7(INCR(cons(0, n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, z0)) -> c7(INCR(cons(0, n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(activate(x1)))), ACTIVATE(x1)) by ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__zeros, n__incr(z0))) -> c7(INCR(cons(zeros, n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(n__zeros, n__adx(z0))) -> c7(INCR(cons(zeros, n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(n__zeros, z0)) -> c7(INCR(cons(zeros, n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) by ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__s(x0), n__incr(z0))) -> c7(INCR(cons(s(x0), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(n__s(x0), n__adx(z0))) -> c7(INCR(cons(s(x0), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(n__s(x0), z0)) -> c7(INCR(cons(s(x0), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) by ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(x0), n__incr(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(n__incr(x0), n__adx(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(n__incr(x0), z0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) by ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__adx(x0), n__incr(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), n__adx(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(n__adx(x0), z0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(z0))), ACTIVATE(z0)) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0))), ACTIVATE(n__0)) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_2, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(activate(x1)))), ACTIVATE(x1)) by ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))), ACTIVATE(n__s(z0))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(x0, n__adx(incr(activate(z0))))), ACTIVATE(n__incr(z0))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(x0, n__adx(adx(activate(z0))))), ACTIVATE(n__adx(z0))) ADX(cons(x0, z0)) -> c7(INCR(cons(x0, n__adx(z0))), ACTIVATE(z0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))), ACTIVATE(n__s(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0))), ACTIVATE(n__0)) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros))), ACTIVATE(n__zeros)) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0)))), ACTIVATE(n__s(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(0)))) by ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c7(INCR(cons(s(z0), n__adx(0)))) ADX(cons(n__incr(z0), n__0)) -> c7(INCR(cons(incr(activate(z0)), n__adx(0)))) ADX(cons(n__adx(z0), n__0)) -> c7(INCR(cons(adx(activate(z0)), n__adx(0)))) ADX(cons(z0, n__0)) -> c7(INCR(cons(z0, n__adx(0)))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(zeros)))) by ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c7(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(n__incr(z0), n__zeros)) -> c7(INCR(cons(incr(activate(z0)), n__adx(zeros)))) ADX(cons(n__adx(z0), n__zeros)) -> c7(INCR(cons(adx(activate(z0)), n__adx(zeros)))) ADX(cons(z0, n__zeros)) -> c7(INCR(cons(z0, n__adx(zeros)))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ADX_1, ACTIVATE_1 Compound Symbols: c3_1, c4_1, c7_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(s(z0))))) by ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ADX(cons(n__0, n__s(x1))) -> c7(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c7(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c7(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(n__incr(z0), n__s(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(s(x1))))) ADX(cons(n__adx(z0), n__s(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(s(x1))))) ADX(cons(z0, n__s(x1))) -> c7(INCR(cons(z0, n__adx(s(x1))))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(activate(z0))), ACTIVATE(n__incr(z0))) by ACTIVATE(n__incr(n__incr(x0))) -> c16(INCR(n__incr(activate(x0))), ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(x0))) -> c16(INCR(n__incr(activate(x0))), ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(x0))) -> c16(INCR(n__incr(activate(x0))), ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(activate(z0))), ACTIVATE(n__adx(z0))) by ACTIVATE(n__incr(n__adx(x0))) -> c16(INCR(n__adx(activate(x0))), ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(INCR(n__adx(activate(x0))), ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(INCR(n__adx(activate(x0))), ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__incr(n__0)) -> c16(INCR(0)) by ACTIVATE(n__incr(n__0)) -> c16(INCR(n__0)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__0)) -> c16(INCR(n__0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__0)) -> c16(INCR(n__0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ACTIVATE(n__incr(n__0)) -> c16(INCR(n__0)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__incr(n__zeros)) -> c16(INCR(zeros)) by ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(n__zeros)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(n__zeros)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(n__zeros)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ACTIVATE(n__incr(n__zeros)) -> c16(INCR(n__zeros)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c16_1, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(s(z0))) by ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(n__s(z0))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(n__s(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(n__s(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ACTIVATE(n__incr(n__s(z0))) -> c16(INCR(n__s(z0))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(activate(z0))), ACTIVATE(n__incr(z0))) by ACTIVATE(n__adx(n__incr(x0))) -> c17(ADX(n__incr(activate(x0))), ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ADX(n__incr(activate(x0))), ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ADX(n__incr(activate(x0))), ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(activate(z0))), ACTIVATE(n__adx(z0))) by ACTIVATE(n__adx(n__adx(x0))) -> c17(ADX(n__adx(activate(x0))), ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ADX(n__adx(activate(x0))), ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ADX(n__adx(activate(x0))), ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__adx(n__0)) -> c17(ADX(0)) by ACTIVATE(n__adx(n__0)) -> c17(ADX(n__0)) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__0)) -> c17(ADX(n__0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__0)) -> c17(ADX(n__0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (173) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ACTIVATE(n__adx(n__0)) -> c17(ADX(n__0)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__adx(n__zeros)) -> c17(ADX(zeros)) by ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(n__zeros)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(n__zeros)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(n__zeros)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ACTIVATE(n__adx(n__zeros)) -> c17(ADX(n__zeros)) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c17_1, c6_2, c6_1, c7_2, c7_1, c16_1 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(s(z0))) by ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(n__s(z0))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(n__s(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(n__s(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c6_2, c6_1, c7_2, c7_1, c16_1, c17_1 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ACTIVATE(n__adx(n__s(z0))) -> c17(ADX(n__s(z0))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c6_2, c6_1, c7_2, c7_1, c16_1, c17_1 ---------------------------------------- (183) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) by ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c6_2, c6_1, c7_2, c7_1, c16_1, c17_1 ---------------------------------------- (185) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) by ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c6_2, c6_1, c7_2, c7_1, c16_1, c17_1 ---------------------------------------- (187) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) by ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0)) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c6_2, c6_1, c7_2, c7_1, c16_1, c17_1 ---------------------------------------- (189) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) by ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0)))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0)))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0)))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c6_2, c6_1, c7_2, c7_1, c16_1, c17_1 ---------------------------------------- (191) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) by ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0)))) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__0) -> 0 activate(n__zeros) -> zeros activate(n__s(z0)) -> s(z0) activate(n__incr(z0)) -> incr(activate(z0)) activate(n__adx(z0)) -> adx(activate(z0)) activate(z0) -> z0 0 -> n__0 zeros -> cons(n__0, n__zeros) zeros -> n__zeros s(z0) -> n__s(z0) incr(cons(z0, z1)) -> cons(n__s(activate(z0)), n__incr(activate(z1))) incr(z0) -> n__incr(z0) adx(cons(z0, z1)) -> incr(cons(activate(z0), n__adx(activate(z1)))) adx(z0) -> n__adx(z0) Tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0)))) S tuples: INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) ACTIVATE(n__incr(z0)) -> c16(INCR(z0), ACTIVATE(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0), ACTIVATE(z0)) ADX(cons(x0, n__0)) -> c6(INCR(cons(activate(x0), n__adx(n__0))), ACTIVATE(x0)) ADX(cons(n__s(z0), n__0)) -> c6(INCR(cons(s(z0), n__adx(0)))) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__zeros)) -> c6(INCR(cons(activate(x0), n__adx(n__zeros))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__zeros)) -> c6(INCR(cons(incr(activate(z0)), n__adx(zeros))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__zeros)) -> c6(INCR(cons(adx(activate(z0)), n__adx(zeros))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__zeros)) -> c6(INCR(cons(z0, n__adx(zeros))), ACTIVATE(z0)) ADX(cons(n__0, n__zeros)) -> c6(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__zeros, n__zeros)) -> c6(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__s(z0), n__zeros)) -> c6(INCR(cons(s(z0), n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c6(INCR(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__s(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__s(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(s(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__s(x1))) -> c6(INCR(cons(z0, n__adx(s(x1)))), ACTIVATE(z0)) ADX(cons(n__0, n__s(x1))) -> c6(INCR(cons(0, n__adx(s(x1))))) ADX(cons(n__zeros, n__s(x1))) -> c6(INCR(cons(zeros, n__adx(s(x1))))) ADX(cons(n__s(z0), n__s(x1))) -> c6(INCR(cons(s(z0), n__adx(s(x1))))) ADX(cons(x0, n__incr(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__0))) -> c6(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__incr(z0))) -> c6(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__incr(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__incr(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__incr(x1))) -> c6(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__incr(x1))) -> c6(INCR(cons(0, n__adx(incr(activate(x1)))))) ADX(cons(n__zeros, n__incr(x1))) -> c6(INCR(cons(zeros, n__adx(incr(activate(x1)))))) ADX(cons(n__s(z0), n__incr(x1))) -> c6(INCR(cons(s(z0), n__adx(incr(activate(x1)))))) ADX(cons(x0, n__adx(x1))) -> c6(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__0))) -> c6(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__zeros))) -> c6(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__s(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__incr(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(n__adx(z0)))) -> c6(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(x0)) ADX(cons(x0, n__adx(z0))) -> c6(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(x0)) ADX(cons(n__incr(z0), n__adx(x1))) -> c6(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__adx(x1))) -> c6(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__adx(x1))) -> c6(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(z0)) ADX(cons(n__0, n__adx(x1))) -> c6(INCR(cons(0, n__adx(adx(activate(x1)))))) ADX(cons(n__zeros, n__adx(x1))) -> c6(INCR(cons(zeros, n__adx(adx(activate(x1)))))) ADX(cons(n__s(z0), n__adx(x1))) -> c6(INCR(cons(s(z0), n__adx(adx(activate(x1)))))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(n__adx(z0))) ADX(cons(z0, x1)) -> c6(INCR(cons(z0, n__adx(x1))), ACTIVATE(z0)) ADX(cons(n__0, x1)) -> c6(INCR(cons(0, n__adx(x1)))) ADX(cons(n__zeros, x1)) -> c6(INCR(cons(zeros, n__adx(x1)))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(s(z0), n__adx(x1)))) ADX(cons(n__incr(x0), x1)) -> c6(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__incr(x0))) ADX(cons(n__incr(n__0), x1)) -> c6(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(n__incr(n__0))) ADX(cons(n__incr(n__zeros), x1)) -> c6(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(n__incr(n__s(z0)), x1)) -> c6(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(n__incr(n__incr(z0)), x1)) -> c6(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(n__incr(n__adx(z0)), x1)) -> c6(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(n__incr(z0), x1)) -> c6(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(x0), x1)) -> c6(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(n__adx(x0))) ADX(cons(n__adx(n__0), x1)) -> c6(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(n__adx(n__0))) ADX(cons(n__adx(n__zeros), x1)) -> c6(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(n__adx(n__s(z0)), x1)) -> c6(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(n__adx(n__incr(z0)), x1)) -> c6(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(n__adx(n__adx(z0)), x1)) -> c6(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(n__adx(z0), x1)) -> c6(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, x0)) -> c6(INCR(cons(n__0, n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0))))) ADX(cons(n__zeros, x0)) -> c6(INCR(cons(n__zeros, n__adx(activate(x0))))) ADX(cons(n__s(z0), x1)) -> c6(INCR(cons(n__s(z0), n__adx(activate(x1))))) ADX(cons(x0, n__incr(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__incr(n__0))) -> c7(INCR(cons(activate(x0), n__adx(incr(0)))), ACTIVATE(n__incr(n__0))) ADX(cons(x0, n__incr(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(incr(zeros)))), ACTIVATE(n__incr(n__zeros))) ADX(cons(x0, n__incr(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(s(z0))))), ACTIVATE(n__incr(n__s(z0)))) ADX(cons(x0, n__incr(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(incr(activate(z0)))))), ACTIVATE(n__incr(n__incr(z0)))) ADX(cons(x0, n__incr(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(incr(adx(activate(z0)))))), ACTIVATE(n__incr(n__adx(z0)))) ADX(cons(x0, n__incr(z0))) -> c7(INCR(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE(n__incr(z0))) ADX(cons(n__0, n__incr(x1))) -> c7(INCR(cons(0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__zeros, n__incr(x1))) -> c7(INCR(cons(zeros, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__s(z0), n__incr(x1))) -> c7(INCR(cons(s(z0), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__incr(z0), n__incr(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(n__adx(z0), n__incr(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(z0, n__incr(x1))) -> c7(INCR(cons(z0, n__adx(incr(activate(x1))))), ACTIVATE(n__incr(x1))) ADX(cons(x0, n__adx(x1))) -> c7(INCR(cons(activate(x0), n__adx(n__adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(x0, n__adx(n__0))) -> c7(INCR(cons(activate(x0), n__adx(adx(0)))), ACTIVATE(n__adx(n__0))) ADX(cons(x0, n__adx(n__zeros))) -> c7(INCR(cons(activate(x0), n__adx(adx(zeros)))), ACTIVATE(n__adx(n__zeros))) ADX(cons(x0, n__adx(n__s(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(s(z0))))), ACTIVATE(n__adx(n__s(z0)))) ADX(cons(x0, n__adx(n__incr(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(incr(activate(z0)))))), ACTIVATE(n__adx(n__incr(z0)))) ADX(cons(x0, n__adx(n__adx(z0)))) -> c7(INCR(cons(activate(x0), n__adx(adx(adx(activate(z0)))))), ACTIVATE(n__adx(n__adx(z0)))) ADX(cons(x0, n__adx(z0))) -> c7(INCR(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE(n__adx(z0))) ADX(cons(n__0, n__adx(x1))) -> c7(INCR(cons(0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__zeros, n__adx(x1))) -> c7(INCR(cons(zeros, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__s(z0), n__adx(x1))) -> c7(INCR(cons(s(z0), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__incr(z0), n__adx(x1))) -> c7(INCR(cons(incr(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__adx(z0), n__adx(x1))) -> c7(INCR(cons(adx(activate(z0)), n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(z0, n__adx(x1))) -> c7(INCR(cons(z0, n__adx(adx(activate(x1))))), ACTIVATE(n__adx(x1))) ADX(cons(n__0, x1)) -> c7(INCR(cons(0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__zeros, x1)) -> c7(INCR(cons(zeros, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(s(z0), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(activate(z0)), n__adx(x1))), ACTIVATE(x1)) ADX(cons(z0, x1)) -> c7(INCR(cons(z0, n__adx(x1))), ACTIVATE(x1)) ADX(cons(n__0, x0)) -> c7(INCR(cons(n__0, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__0, n__0)) -> c7(INCR(cons(0, n__adx(0)))) ADX(cons(n__0, n__zeros)) -> c7(INCR(cons(0, n__adx(zeros)))) ADX(cons(n__0, n__s(z0))) -> c7(INCR(cons(0, n__adx(s(z0))))) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, x0)) -> c7(INCR(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE(x0)) ADX(cons(n__zeros, n__0)) -> c7(INCR(cons(zeros, n__adx(0)))) ADX(cons(n__zeros, n__zeros)) -> c7(INCR(cons(zeros, n__adx(zeros)))) ADX(cons(n__zeros, n__s(z0))) -> c7(INCR(cons(zeros, n__adx(s(z0))))) ADX(cons(n__s(z0), x1)) -> c7(INCR(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__s(x0), n__0)) -> c7(INCR(cons(s(x0), n__adx(0)))) ADX(cons(n__s(x0), n__zeros)) -> c7(INCR(cons(s(x0), n__adx(zeros)))) ADX(cons(n__s(x0), n__s(z0))) -> c7(INCR(cons(s(x0), n__adx(s(z0))))) ADX(cons(n__incr(x0), x1)) -> c7(INCR(cons(n__incr(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__0), x1)) -> c7(INCR(cons(incr(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__zeros), x1)) -> c7(INCR(cons(incr(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__s(z0)), x1)) -> c7(INCR(cons(incr(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__incr(z0)), x1)) -> c7(INCR(cons(incr(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(n__adx(z0)), x1)) -> c7(INCR(cons(incr(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(z0), x1)) -> c7(INCR(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__incr(x0), n__0)) -> c7(INCR(cons(incr(activate(x0)), n__adx(0)))) ADX(cons(n__incr(x0), n__zeros)) -> c7(INCR(cons(incr(activate(x0)), n__adx(zeros)))) ADX(cons(n__incr(x0), n__s(z0))) -> c7(INCR(cons(incr(activate(x0)), n__adx(s(z0))))) ADX(cons(n__adx(x0), x1)) -> c7(INCR(cons(n__adx(activate(x0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__0), x1)) -> c7(INCR(cons(adx(0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__zeros), x1)) -> c7(INCR(cons(adx(zeros), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__s(z0)), x1)) -> c7(INCR(cons(adx(s(z0)), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__incr(z0)), x1)) -> c7(INCR(cons(adx(incr(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(n__adx(z0)), x1)) -> c7(INCR(cons(adx(adx(activate(z0))), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(z0), x1)) -> c7(INCR(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE(x1)) ADX(cons(n__adx(x0), n__0)) -> c7(INCR(cons(adx(activate(x0)), n__adx(0)))) ADX(cons(n__adx(x0), n__zeros)) -> c7(INCR(cons(adx(activate(x0)), n__adx(zeros)))) ADX(cons(n__adx(x0), n__s(z0))) -> c7(INCR(cons(adx(activate(x0)), n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(x0, n__adx(0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(x0, n__adx(zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(x0, n__adx(s(z0))))) ADX(cons(x0, n__0)) -> c7(INCR(cons(activate(x0), n__adx(n__0)))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(cons(n__0, n__zeros))))) ADX(cons(x0, n__zeros)) -> c7(INCR(cons(activate(x0), n__adx(n__zeros)))) ADX(cons(x0, n__s(z0))) -> c7(INCR(cons(activate(x0), n__adx(n__s(z0))))) ACTIVATE(n__incr(n__incr(n__0))) -> c16(INCR(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__incr(n__incr(n__zeros))) -> c16(INCR(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__incr(n__incr(n__s(z0)))) -> c16(INCR(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__incr(n__incr(n__incr(z0)))) -> c16(INCR(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__incr(n__incr(n__adx(z0)))) -> c16(INCR(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__incr(n__incr(z0))) -> c16(INCR(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__incr(n__incr(x0))) -> c16(ACTIVATE(n__incr(x0))) ACTIVATE(n__incr(n__adx(n__0))) -> c16(INCR(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__incr(n__adx(n__zeros))) -> c16(INCR(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__incr(n__adx(n__s(z0)))) -> c16(INCR(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__incr(n__adx(n__incr(z0)))) -> c16(INCR(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__incr(n__adx(n__adx(z0)))) -> c16(INCR(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__incr(n__adx(z0))) -> c16(INCR(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__incr(n__adx(x0))) -> c16(ACTIVATE(n__adx(x0))) ACTIVATE(n__incr(n__zeros)) -> c16(INCR(cons(n__0, n__zeros))) ACTIVATE(n__adx(n__incr(n__0))) -> c17(ADX(incr(0)), ACTIVATE(n__incr(n__0))) ACTIVATE(n__adx(n__incr(n__zeros))) -> c17(ADX(incr(zeros)), ACTIVATE(n__incr(n__zeros))) ACTIVATE(n__adx(n__incr(n__s(z0)))) -> c17(ADX(incr(s(z0))), ACTIVATE(n__incr(n__s(z0)))) ACTIVATE(n__adx(n__incr(n__incr(z0)))) -> c17(ADX(incr(incr(activate(z0)))), ACTIVATE(n__incr(n__incr(z0)))) ACTIVATE(n__adx(n__incr(n__adx(z0)))) -> c17(ADX(incr(adx(activate(z0)))), ACTIVATE(n__incr(n__adx(z0)))) ACTIVATE(n__adx(n__incr(z0))) -> c17(ADX(incr(z0)), ACTIVATE(n__incr(z0))) ACTIVATE(n__adx(n__incr(x0))) -> c17(ACTIVATE(n__incr(x0))) ACTIVATE(n__adx(n__adx(n__0))) -> c17(ADX(adx(0)), ACTIVATE(n__adx(n__0))) ACTIVATE(n__adx(n__adx(n__zeros))) -> c17(ADX(adx(zeros)), ACTIVATE(n__adx(n__zeros))) ACTIVATE(n__adx(n__adx(n__s(z0)))) -> c17(ADX(adx(s(z0))), ACTIVATE(n__adx(n__s(z0)))) ACTIVATE(n__adx(n__adx(n__incr(z0)))) -> c17(ADX(adx(incr(activate(z0)))), ACTIVATE(n__adx(n__incr(z0)))) ACTIVATE(n__adx(n__adx(n__adx(z0)))) -> c17(ADX(adx(adx(activate(z0)))), ACTIVATE(n__adx(n__adx(z0)))) ACTIVATE(n__adx(n__adx(z0))) -> c17(ADX(adx(z0)), ACTIVATE(n__adx(z0))) ACTIVATE(n__adx(n__adx(x0))) -> c17(ACTIVATE(n__adx(x0))) ACTIVATE(n__adx(n__zeros)) -> c17(ADX(cons(n__0, n__zeros))) ADX(cons(n__incr(z0), n__0)) -> c6(INCR(cons(incr(activate(z0)), n__adx(n__0))), ACTIVATE(n__incr(z0))) ADX(cons(n__adx(z0), n__0)) -> c6(INCR(cons(adx(activate(z0)), n__adx(n__0))), ACTIVATE(n__adx(z0))) ADX(cons(z0, n__0)) -> c6(INCR(cons(z0, n__adx(n__0))), ACTIVATE(z0)) ADX(cons(n__0, n__0)) -> c6(INCR(cons(0, n__adx(n__0)))) ADX(cons(n__zeros, n__0)) -> c6(INCR(cons(zeros, n__adx(n__0)))) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR_1, ACTIVATE_1, ADX_1 Compound Symbols: c3_1, c4_1, c16_2, c17_2, c6_2, c6_1, c7_2, c7_1, c16_1, c17_1 ---------------------------------------- (193) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (194) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: nats -> adx(zeros) [1] zeros -> cons(n__0, n__zeros) [1] incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1] adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1] hd(cons(X, Y)) -> activate(X) [1] tl(cons(X, Y)) -> activate(Y) [1] 0 -> n__0 [1] zeros -> n__zeros [1] s(X) -> n__s(X) [1] incr(X) -> n__incr(X) [1] adx(X) -> n__adx(X) [1] activate(n__0) -> 0 [1] activate(n__zeros) -> zeros [1] activate(n__s(X)) -> s(X) [1] activate(n__incr(X)) -> incr(activate(X)) [1] activate(n__adx(X)) -> adx(activate(X)) [1] activate(X) -> X [1] Rewrite Strategy: INNERMOST ---------------------------------------- (195) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: 0 => 0' ---------------------------------------- (196) 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: nats -> adx(zeros) [1] zeros -> cons(n__0, n__zeros) [1] incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1] adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1] hd(cons(X, Y)) -> activate(X) [1] tl(cons(X, Y)) -> activate(Y) [1] 0' -> n__0 [1] zeros -> n__zeros [1] s(X) -> n__s(X) [1] incr(X) -> n__incr(X) [1] adx(X) -> n__adx(X) [1] activate(n__0) -> 0' [1] activate(n__zeros) -> zeros [1] activate(n__s(X)) -> s(X) [1] activate(n__incr(X)) -> incr(activate(X)) [1] activate(n__adx(X)) -> adx(activate(X)) [1] activate(X) -> X [1] Rewrite Strategy: INNERMOST ---------------------------------------- (197) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (198) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: nats -> adx(zeros) [1] zeros -> cons(n__0, n__zeros) [1] incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1] adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1] hd(cons(X, Y)) -> activate(X) [1] tl(cons(X, Y)) -> activate(Y) [1] 0' -> n__0 [1] zeros -> n__zeros [1] s(X) -> n__s(X) [1] incr(X) -> n__incr(X) [1] adx(X) -> n__adx(X) [1] activate(n__0) -> 0' [1] activate(n__zeros) -> zeros [1] activate(n__s(X)) -> s(X) [1] activate(n__incr(X)) -> incr(activate(X)) [1] activate(n__adx(X)) -> adx(activate(X)) [1] activate(X) -> X [1] The TRS has the following type information: nats :: n__0:n__zeros:cons:n__s:n__incr:n__adx adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx cons :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__0 :: n__0:n__zeros:cons:n__s:n__incr:n__adx n__zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx activate :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx 0' :: n__0:n__zeros:cons:n__s:n__incr:n__adx s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx Rewrite Strategy: INNERMOST ---------------------------------------- (199) 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: nats hd_1 tl_1 (c) The following functions are completely defined: zeros activate_1 adx_1 incr_1 0' s_1 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (200) 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: nats -> adx(zeros) [1] zeros -> cons(n__0, n__zeros) [1] incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1] adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1] hd(cons(X, Y)) -> activate(X) [1] tl(cons(X, Y)) -> activate(Y) [1] 0' -> n__0 [1] zeros -> n__zeros [1] s(X) -> n__s(X) [1] incr(X) -> n__incr(X) [1] adx(X) -> n__adx(X) [1] activate(n__0) -> 0' [1] activate(n__zeros) -> zeros [1] activate(n__s(X)) -> s(X) [1] activate(n__incr(X)) -> incr(activate(X)) [1] activate(n__adx(X)) -> adx(activate(X)) [1] activate(X) -> X [1] The TRS has the following type information: nats :: n__0:n__zeros:cons:n__s:n__incr:n__adx adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx cons :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__0 :: n__0:n__zeros:cons:n__s:n__incr:n__adx n__zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx activate :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx 0' :: n__0:n__zeros:cons:n__s:n__incr:n__adx s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx Rewrite Strategy: INNERMOST ---------------------------------------- (201) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (202) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: nats -> adx(cons(n__0, n__zeros)) [2] nats -> adx(n__zeros) [2] zeros -> cons(n__0, n__zeros) [1] incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1] adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1] hd(cons(X, Y)) -> activate(X) [1] tl(cons(X, Y)) -> activate(Y) [1] 0' -> n__0 [1] zeros -> n__zeros [1] s(X) -> n__s(X) [1] incr(X) -> n__incr(X) [1] adx(X) -> n__adx(X) [1] activate(n__0) -> 0' [1] activate(n__zeros) -> zeros [1] activate(n__s(X)) -> s(X) [1] activate(n__incr(n__0)) -> incr(0') [2] activate(n__incr(n__zeros)) -> incr(zeros) [2] activate(n__incr(n__s(X20))) -> incr(s(X20)) [2] activate(n__incr(n__incr(X21))) -> incr(incr(activate(X21))) [2] activate(n__incr(n__adx(X22))) -> incr(adx(activate(X22))) [2] activate(n__incr(X)) -> incr(X) [2] activate(n__adx(n__0)) -> adx(0') [2] activate(n__adx(n__zeros)) -> adx(zeros) [2] activate(n__adx(n__s(X23))) -> adx(s(X23)) [2] activate(n__adx(n__incr(X24))) -> adx(incr(activate(X24))) [2] activate(n__adx(n__adx(X25))) -> adx(adx(activate(X25))) [2] activate(n__adx(X)) -> adx(X) [2] activate(X) -> X [1] The TRS has the following type information: nats :: n__0:n__zeros:cons:n__s:n__incr:n__adx adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx cons :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__0 :: n__0:n__zeros:cons:n__s:n__incr:n__adx n__zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx activate :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx n__adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx 0' :: n__0:n__zeros:cons:n__s:n__incr:n__adx s :: n__0:n__zeros:cons:n__s:n__incr:n__adx -> n__0:n__zeros:cons:n__s:n__incr:n__adx Rewrite Strategy: INNERMOST ---------------------------------------- (203) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: n__0 => 0 n__zeros => 1 ---------------------------------------- (204) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 1 }-> 0 :|: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 1 }-> zeros :|: z = 1 activate(z) -{ 1 }-> s(X) :|: z = 1 + X, X >= 0 activate(z) -{ 2 }-> incr(X) :|: z = 1 + X, X >= 0 activate(z) -{ 2 }-> incr(zeros) :|: z = 1 + 1 activate(z) -{ 2 }-> incr(s(X20)) :|: z = 1 + (1 + X20), X20 >= 0 activate(z) -{ 2 }-> incr(incr(activate(X21))) :|: X21 >= 0, z = 1 + (1 + X21) activate(z) -{ 2 }-> incr(adx(activate(X22))) :|: X22 >= 0, z = 1 + (1 + X22) activate(z) -{ 2 }-> incr(0') :|: z = 1 + 0 activate(z) -{ 2 }-> adx(X) :|: z = 1 + X, X >= 0 activate(z) -{ 2 }-> adx(zeros) :|: z = 1 + 1 activate(z) -{ 2 }-> adx(s(X23)) :|: z = 1 + (1 + X23), X23 >= 0 activate(z) -{ 2 }-> adx(incr(activate(X24))) :|: z = 1 + (1 + X24), X24 >= 0 activate(z) -{ 2 }-> adx(adx(activate(X25))) :|: z = 1 + (1 + X25), X25 >= 0 activate(z) -{ 2 }-> adx(0') :|: z = 1 + 0 activate(z) -{ 1 }-> 0' :|: z = 0 adx(z) -{ 1 }-> incr(1 + activate(X) + (1 + activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0 adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X hd(z) -{ 1 }-> activate(X) :|: Y >= 0, z = 1 + X + Y, X >= 0 incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X incr(z) -{ 1 }-> 1 + (1 + activate(X)) + (1 + activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 nats -{ 2 }-> adx(1) :|: nats -{ 2 }-> adx(1 + 0 + 1) :|: s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X tl(z) -{ 1 }-> activate(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 zeros -{ 1 }-> 1 :|: zeros -{ 1 }-> 1 + 0 + 1 :|: ---------------------------------------- (205) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: zeros -{ 1 }-> 1 :|: zeros -{ 1 }-> 1 + 0 + 1 :|: 0' -{ 1 }-> 0 :|: s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (206) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 1 }-> 0 :|: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 2 }-> incr(X) :|: z = 1 + X, X >= 0 activate(z) -{ 2 }-> incr(incr(activate(X21))) :|: X21 >= 0, z = 1 + (1 + X21) activate(z) -{ 2 }-> incr(adx(activate(X22))) :|: X22 >= 0, z = 1 + (1 + X22) activate(z) -{ 3 }-> incr(1) :|: z = 1 + 1 activate(z) -{ 3 }-> incr(0) :|: z = 1 + 0 activate(z) -{ 3 }-> incr(1 + X) :|: z = 1 + (1 + X20), X20 >= 0, X >= 0, X20 = X activate(z) -{ 3 }-> incr(1 + 0 + 1) :|: z = 1 + 1 activate(z) -{ 2 }-> adx(X) :|: z = 1 + X, X >= 0 activate(z) -{ 2 }-> adx(incr(activate(X24))) :|: z = 1 + (1 + X24), X24 >= 0 activate(z) -{ 2 }-> adx(adx(activate(X25))) :|: z = 1 + (1 + X25), X25 >= 0 activate(z) -{ 3 }-> adx(1) :|: z = 1 + 1 activate(z) -{ 3 }-> adx(0) :|: z = 1 + 0 activate(z) -{ 3 }-> adx(1 + X) :|: z = 1 + (1 + X23), X23 >= 0, X >= 0, X23 = X activate(z) -{ 3 }-> adx(1 + 0 + 1) :|: z = 1 + 1 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 2 }-> 0 :|: z = 0 activate(z) -{ 2 }-> 1 + X' :|: z = 1 + X, X >= 0, X' >= 0, X = X' activate(z) -{ 2 }-> 1 + 0 + 1 :|: z = 1 adx(z) -{ 1 }-> incr(1 + activate(X) + (1 + activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0 adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X hd(z) -{ 1 }-> activate(X) :|: Y >= 0, z = 1 + X + Y, X >= 0 incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X incr(z) -{ 1 }-> 1 + (1 + activate(X)) + (1 + activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 nats -{ 2 }-> adx(1) :|: nats -{ 2 }-> adx(1 + 0 + 1) :|: s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X tl(z) -{ 1 }-> activate(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 zeros -{ 1 }-> 1 :|: zeros -{ 1 }-> 1 + 0 + 1 :|: ---------------------------------------- (207) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (208) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 1 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> incr(incr(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> incr(adx(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 3 }-> incr(1) :|: z = 1 + 1 activate(z) -{ 3 }-> incr(0) :|: z = 1 + 0 activate(z) -{ 2 }-> incr(z - 1) :|: z - 1 >= 0 activate(z) -{ 3 }-> incr(1 + X) :|: z - 2 >= 0, X >= 0, z - 2 = X activate(z) -{ 3 }-> incr(1 + 0 + 1) :|: z = 1 + 1 activate(z) -{ 2 }-> adx(incr(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> adx(adx(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 3 }-> adx(1) :|: z = 1 + 1 activate(z) -{ 3 }-> adx(0) :|: z = 1 + 0 activate(z) -{ 2 }-> adx(z - 1) :|: z - 1 >= 0 activate(z) -{ 3 }-> adx(1 + X) :|: z - 2 >= 0, X >= 0, z - 2 = X activate(z) -{ 3 }-> adx(1 + 0 + 1) :|: z = 1 + 1 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 2 }-> 0 :|: z = 0 activate(z) -{ 2 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> 1 + 0 + 1 :|: z = 1 adx(z) -{ 1 }-> incr(1 + activate(X) + (1 + activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0 adx(z) -{ 1 }-> 1 + z :|: z >= 0 hd(z) -{ 1 }-> activate(X) :|: Y >= 0, z = 1 + X + Y, X >= 0 incr(z) -{ 1 }-> 1 + z :|: z >= 0 incr(z) -{ 1 }-> 1 + (1 + activate(X)) + (1 + activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 nats -{ 2 }-> adx(1) :|: nats -{ 2 }-> adx(1 + 0 + 1) :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 tl(z) -{ 1 }-> activate(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 zeros -{ 1 }-> 1 :|: zeros -{ 1 }-> 1 + 0 + 1 :|: ---------------------------------------- (209) 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: hd(v0) -> null_hd [0] tl(v0) -> null_tl [0] And the following fresh constants: null_hd, null_tl ---------------------------------------- (210) 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: nats -> adx(zeros) [1] zeros -> cons(n__0, n__zeros) [1] incr(cons(X, Y)) -> cons(n__s(activate(X)), n__incr(activate(Y))) [1] adx(cons(X, Y)) -> incr(cons(activate(X), n__adx(activate(Y)))) [1] hd(cons(X, Y)) -> activate(X) [1] tl(cons(X, Y)) -> activate(Y) [1] 0' -> n__0 [1] zeros -> n__zeros [1] s(X) -> n__s(X) [1] incr(X) -> n__incr(X) [1] adx(X) -> n__adx(X) [1] activate(n__0) -> 0' [1] activate(n__zeros) -> zeros [1] activate(n__s(X)) -> s(X) [1] activate(n__incr(X)) -> incr(activate(X)) [1] activate(n__adx(X)) -> adx(activate(X)) [1] activate(X) -> X [1] hd(v0) -> null_hd [0] tl(v0) -> null_tl [0] The TRS has the following type information: nats :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl cons :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl n__0 :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl n__zeros :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl n__s :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl activate :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl n__incr :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl n__adx :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl 0' :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl s :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl -> n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl null_hd :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl null_tl :: n__0:n__zeros:cons:n__s:n__incr:n__adx:null_hd:null_tl Rewrite Strategy: INNERMOST ---------------------------------------- (211) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: n__0 => 0 n__zeros => 1 null_hd => 0 null_tl => 0 ---------------------------------------- (212) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 1 }-> 0 :|: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 1 }-> zeros :|: z = 1 activate(z) -{ 1 }-> s(X) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> incr(activate(X)) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> adx(activate(X)) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> 0' :|: z = 0 adx(z) -{ 1 }-> incr(1 + activate(X) + (1 + activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0 adx(z) -{ 1 }-> 1 + X :|: X >= 0, z = X hd(z) -{ 1 }-> activate(X) :|: Y >= 0, z = 1 + X + Y, X >= 0 hd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X incr(z) -{ 1 }-> 1 + (1 + activate(X)) + (1 + activate(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 nats -{ 1 }-> adx(zeros) :|: s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X tl(z) -{ 1 }-> activate(Y) :|: Y >= 0, z = 1 + X + Y, X >= 0 tl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 zeros -{ 1 }-> 1 :|: zeros -{ 1 }-> 1 + 0 + 1 :|: Only complete derivations are relevant for the runtime complexity.