KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.trs # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). (0) CpxRelTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxRelTRS (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) typed CpxTrs (7) OrderProof [LOWER BOUND(ID), 15 ms] (8) typed CpxTrs (9) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (10) CpxTRS (11) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxWeightedTrs (13) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxWeightedTrs (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxTypedWeightedTrs (17) CompletionProof [UPPER BOUND(ID), 0 ms] (18) CpxTypedWeightedCompleteTrs (19) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) InliningProof [UPPER BOUND(ID), 403 ms] (24) CpxRNTS (25) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxRNTS (27) CompletionProof [UPPER BOUND(ID), 0 ms] (28) CpxTypedWeightedCompleteTrs (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (32) CdtProblem (33) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (34) CdtProblem (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem ---------------------------------------- (0) 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(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(z0) activate(n__adx(z0)) -> adx(z0) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(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(z0) activate(n__adx(z0)) -> adx(z0) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (3) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (4) 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(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(z0) activate(n__adx(z0)) -> adx(z0) activate(z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (5) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (6) 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(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(z0) activate(n__adx(z0)) -> adx(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 c17 :: c6:c7:c8 -> 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 ---------------------------------------- (7) 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 = adx activate = incr adx = incr ---------------------------------------- (8) 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(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(z0) activate(n__adx(z0)) -> adx(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 c17 :: c6:c7:c8 -> 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 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)) 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 = adx activate = incr adx = incr ---------------------------------------- (9) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (10) 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: 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(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(z0) activate(n__adx(z0)) -> adx(z0) activate(z0) -> z0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (11) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (12) 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 -> c(ADX(zeros), ZEROS) [1] ZEROS -> c1 [1] ZEROS -> c2 [1] INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] INCR(z0) -> c5 [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] ADX(z0) -> c8 [1] HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) [1] TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) [1] 0' -> c11 [1] S(z0) -> c12 [1] ACTIVATE(n__0) -> c13(0') [1] ACTIVATE(n__zeros) -> c14(ZEROS) [1] ACTIVATE(n__s(z0)) -> c15(S(z0)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1] ACTIVATE(z0) -> c18 [1] nats -> adx(zeros) [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [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] hd(cons(z0, z1)) -> activate(z0) [0] tl(cons(z0, z1)) -> activate(z1) [0] 0 -> n__0 [0] s(z0) -> n__s(z0) [0] activate(n__0) -> 0 [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(z0) [0] activate(n__adx(z0)) -> adx(z0) [0] activate(z0) -> z0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (13) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: 0 => 0'' ---------------------------------------- (14) 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 -> c(ADX(zeros), ZEROS) [1] ZEROS -> c1 [1] ZEROS -> c2 [1] INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] INCR(z0) -> c5 [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] ADX(z0) -> c8 [1] HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) [1] TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) [1] 0' -> c11 [1] S(z0) -> c12 [1] ACTIVATE(n__0) -> c13(0') [1] ACTIVATE(n__zeros) -> c14(ZEROS) [1] ACTIVATE(n__s(z0)) -> c15(S(z0)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1] ACTIVATE(z0) -> c18 [1] nats -> adx(zeros) [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [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] hd(cons(z0, z1)) -> activate(z0) [0] tl(cons(z0, z1)) -> activate(z1) [0] 0'' -> n__0 [0] s(z0) -> n__s(z0) [0] activate(n__0) -> 0'' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(z0) [0] activate(n__adx(z0)) -> adx(z0) [0] activate(z0) -> z0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (15) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (16) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: NATS -> c(ADX(zeros), ZEROS) [1] ZEROS -> c1 [1] ZEROS -> c2 [1] INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] INCR(z0) -> c5 [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] ADX(z0) -> c8 [1] HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) [1] TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) [1] 0' -> c11 [1] S(z0) -> c12 [1] ACTIVATE(n__0) -> c13(0') [1] ACTIVATE(n__zeros) -> c14(ZEROS) [1] ACTIVATE(n__s(z0)) -> c15(S(z0)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1] ACTIVATE(z0) -> c18 [1] nats -> adx(zeros) [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [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] hd(cons(z0, z1)) -> activate(z0) [0] tl(cons(z0, z1)) -> activate(z1) [0] 0'' -> n__0 [0] s(z0) -> n__s(z0) [0] activate(n__0) -> 0'' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(z0) [0] activate(n__adx(z0)) -> adx(z0) [0] activate(z0) -> z0 [0] The TRS has the following type information: NATS :: c c :: c6:c7:c8 -> c1:c2 -> c ADX :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> c6:c7:c8 zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr ZEROS :: c1:c2 c1 :: c1:c2 c2 :: c1:c2 INCR :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> c3:c4:c5 cons :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr c3 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5 ACTIVATE :: cons:n__adx: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:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr n__adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx: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:n__0:n__zeros:n__s:n__incr -> c9 c9 :: c13:c14:c15:c16:c17:c18 -> c9 TL :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> c10 c10 :: c13:c14:c15:c16:c17:c18 -> c10 0' :: c11 c11 :: c11 S :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> c12 c12 :: c12 n__0 :: cons:n__adx:n__0:n__zeros:n__s:n__incr c13 :: c11 -> c13:c14:c15:c16:c17:c18 n__zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr c14 :: c1:c2 -> c13:c14:c15:c16:c17:c18 n__s :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr c15 :: c12 -> c13:c14:c15:c16:c17:c18 n__incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr c16 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 c17 :: c6:c7:c8 -> c13:c14:c15:c16:c17:c18 c18 :: c13:c14:c15:c16:c17:c18 nats :: cons:n__adx:n__0:n__zeros:n__s:n__incr adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr hd :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr tl :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr 0'' :: cons:n__adx:n__0:n__zeros:n__s:n__incr s :: cons:n__adx:n__0:n__zeros:n__s:n__incr -> cons:n__adx:n__0:n__zeros:n__s:n__incr Rewrite Strategy: INNERMOST ---------------------------------------- (17) 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 ZEROS INCR_1 ADX_1 HD_1 TL_1 0' S_1 ACTIVATE_1 (c) The following functions are completely defined: nats zeros incr_1 adx_1 hd_1 tl_1 0'' s_1 activate_1 Due to the following rules being added: nats -> null_nats [0] zeros -> null_zeros [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] hd(v0) -> null_hd [0] tl(v0) -> null_tl [0] 0'' -> null_0'' [0] s(v0) -> null_s [0] activate(v0) -> null_activate [0] And the following fresh constants: null_nats, null_zeros, null_incr, null_adx, null_hd, null_tl, null_0'', null_s, null_activate, const, const1, const2 ---------------------------------------- (18) 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 -> c(ADX(zeros), ZEROS) [1] ZEROS -> c1 [1] ZEROS -> c2 [1] INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] INCR(z0) -> c5 [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] ADX(z0) -> c8 [1] HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) [1] TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) [1] 0' -> c11 [1] S(z0) -> c12 [1] ACTIVATE(n__0) -> c13(0') [1] ACTIVATE(n__zeros) -> c14(ZEROS) [1] ACTIVATE(n__s(z0)) -> c15(S(z0)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1] ACTIVATE(z0) -> c18 [1] nats -> adx(zeros) [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [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] hd(cons(z0, z1)) -> activate(z0) [0] tl(cons(z0, z1)) -> activate(z1) [0] 0'' -> n__0 [0] s(z0) -> n__s(z0) [0] activate(n__0) -> 0'' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(z0) [0] activate(n__adx(z0)) -> adx(z0) [0] activate(z0) -> z0 [0] nats -> null_nats [0] zeros -> null_zeros [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] hd(v0) -> null_hd [0] tl(v0) -> null_tl [0] 0'' -> null_0'' [0] s(v0) -> null_s [0] activate(v0) -> null_activate [0] The TRS has the following type information: NATS :: c c :: c6:c7:c8 -> c1:c2 -> c ADX :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c6:c7:c8 zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate ZEROS :: c1:c2 c1 :: c1:c2 c2 :: c1:c2 INCR :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c3:c4:c5 cons :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c3 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5 ACTIVATE :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> 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:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate n__adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c7 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8 c8 :: c6:c7:c8 HD :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c9 c9 :: c13:c14:c15:c16:c17:c18 -> c9 TL :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c10 c10 :: c13:c14:c15:c16:c17:c18 -> c10 0' :: c11 c11 :: c11 S :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c12 c12 :: c12 n__0 :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c13 :: c11 -> c13:c14:c15:c16:c17:c18 n__zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c14 :: c1:c2 -> c13:c14:c15:c16:c17:c18 n__s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c15 :: c12 -> c13:c14:c15:c16:c17:c18 n__incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c16 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 c17 :: c6:c7:c8 -> c13:c14:c15:c16:c17:c18 c18 :: c13:c14:c15:c16:c17:c18 nats :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate hd :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate tl :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate 0'' :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_nats :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_hd :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_tl :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_0'' :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_activate :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate const :: c const1 :: c9 const2 :: c10 Rewrite Strategy: INNERMOST ---------------------------------------- (19) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (20) 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 -> c(ADX(cons(n__0, n__zeros)), ZEROS) [1] NATS -> c(ADX(n__zeros), ZEROS) [1] NATS -> c(ADX(null_zeros), ZEROS) [1] ZEROS -> c1 [1] ZEROS -> c2 [1] INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] INCR(z0) -> c5 [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] ADX(z0) -> c8 [1] HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) [1] TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) [1] 0' -> c11 [1] S(z0) -> c12 [1] ACTIVATE(n__0) -> c13(0') [1] ACTIVATE(n__zeros) -> c14(ZEROS) [1] ACTIVATE(n__s(z0)) -> c15(S(z0)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1] ACTIVATE(z0) -> c18 [1] nats -> adx(cons(n__0, n__zeros)) [0] nats -> adx(n__zeros) [0] nats -> adx(null_zeros) [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [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] hd(cons(z0, z1)) -> activate(z0) [0] tl(cons(z0, z1)) -> activate(z1) [0] 0'' -> n__0 [0] s(z0) -> n__s(z0) [0] activate(n__0) -> 0'' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(z0) [0] activate(n__adx(z0)) -> adx(z0) [0] activate(z0) -> z0 [0] nats -> null_nats [0] zeros -> null_zeros [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] hd(v0) -> null_hd [0] tl(v0) -> null_tl [0] 0'' -> null_0'' [0] s(v0) -> null_s [0] activate(v0) -> null_activate [0] The TRS has the following type information: NATS :: c c :: c6:c7:c8 -> c1:c2 -> c ADX :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c6:c7:c8 zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate ZEROS :: c1:c2 c1 :: c1:c2 c2 :: c1:c2 INCR :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c3:c4:c5 cons :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c3 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5 ACTIVATE :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> 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:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate n__adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c7 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8 c8 :: c6:c7:c8 HD :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c9 c9 :: c13:c14:c15:c16:c17:c18 -> c9 TL :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c10 c10 :: c13:c14:c15:c16:c17:c18 -> c10 0' :: c11 c11 :: c11 S :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c12 c12 :: c12 n__0 :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c13 :: c11 -> c13:c14:c15:c16:c17:c18 n__zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c14 :: c1:c2 -> c13:c14:c15:c16:c17:c18 n__s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c15 :: c12 -> c13:c14:c15:c16:c17:c18 n__incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c16 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 c17 :: c6:c7:c8 -> c13:c14:c15:c16:c17:c18 c18 :: c13:c14:c15:c16:c17:c18 nats :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate hd :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate tl :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate 0'' :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_nats :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_hd :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_tl :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_0'' :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_activate :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate const :: c const1 :: c9 const2 :: c10 Rewrite Strategy: INNERMOST ---------------------------------------- (21) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: c1 => 0 c2 => 1 c5 => 0 c8 => 0 c11 => 0 c12 => 0 n__0 => 0 n__zeros => 1 c18 => 0 null_nats => 0 null_zeros => 0 null_incr => 0 null_adx => 0 null_hd => 0 null_tl => 0 null_0'' => 0 null_s => 0 null_activate => 0 const => 0 const1 => 0 const2 => 0 ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 1 }-> 0 :|: 0'' -{ 0 }-> 0 :|: ACTIVATE(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ZEROS :|: z = 1 ACTIVATE(z) -{ 1 }-> 1 + S(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + 0' :|: z = 0 ADX(z) -{ 1 }-> 0 :|: z = 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 HD(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 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 -{ 1 }-> 1 + ADX(1) + ZEROS :|: NATS -{ 1 }-> 1 + ADX(0) + ZEROS :|: NATS -{ 1 }-> 1 + ADX(1 + 0 + 1) + ZEROS :|: S(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 TL(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ZEROS -{ 1 }-> 1 :|: ZEROS -{ 1 }-> 0 :|: 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 }-> adx(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 hd(z) -{ 0 }-> activate(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 hd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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 nats -{ 0 }-> adx(1) :|: nats -{ 0 }-> adx(0) :|: nats -{ 0 }-> adx(1 + 0 + 1) :|: nats -{ 0 }-> 0 :|: s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 tl(z) -{ 0 }-> activate(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 tl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 zeros -{ 0 }-> 1 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: ---------------------------------------- (23) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: ZEROS -{ 1 }-> 0 :|: ZEROS -{ 1 }-> 1 :|: 0' -{ 1 }-> 0 :|: S(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: zeros -{ 0 }-> 1 :|: 0'' -{ 0 }-> 0 :|: s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 ---------------------------------------- (24) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 1 }-> 0 :|: 0'' -{ 0 }-> 0 :|: ACTIVATE(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 2 }-> 1 + 1 :|: z = 1 ACTIVATE(z) -{ 2 }-> 1 + 0 :|: z = 1 ACTIVATE(z) -{ 2 }-> 1 + 0 :|: z = 0 ACTIVATE(z) -{ 2 }-> 1 + 0 :|: z = 1 + z0, z0 >= 0, z0 = z0', z0' >= 0 ADX(z) -{ 1 }-> 0 :|: z = 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 HD(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 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 -{ 2 }-> 1 + ADX(1) + 1 :|: NATS -{ 2 }-> 1 + ADX(1) + 0 :|: NATS -{ 2 }-> 1 + ADX(0) + 1 :|: NATS -{ 2 }-> 1 + ADX(0) + 0 :|: NATS -{ 2 }-> 1 + ADX(1 + 0 + 1) + 1 :|: NATS -{ 2 }-> 1 + ADX(1 + 0 + 1) + 0 :|: S(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 TL(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ZEROS -{ 1 }-> 1 :|: ZEROS -{ 1 }-> 0 :|: activate(z) -{ 0 }-> z0 :|: z = z0, z0 >= 0 activate(z) -{ 0 }-> incr(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> adx(z0) :|: z = 1 + z0, z0 >= 0 activate(z) -{ 0 }-> 1 :|: z = 1 activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 activate(z) -{ 0 }-> 0 :|: z = 1 activate(z) -{ 0 }-> 0 :|: z = 0 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 hd(z) -{ 0 }-> activate(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 hd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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 nats -{ 0 }-> adx(1) :|: nats -{ 0 }-> adx(0) :|: nats -{ 0 }-> adx(1 + 0 + 1) :|: nats -{ 0 }-> 0 :|: s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 tl(z) -{ 0 }-> activate(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 tl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 zeros -{ 0 }-> 1 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: ---------------------------------------- (25) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 1 }-> 0 :|: 0'' -{ 0 }-> 0 :|: ACTIVATE(z) -{ 1 }-> 0 :|: z >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(z - 1) :|: z - 1 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(z - 1) :|: z - 1 >= 0 ACTIVATE(z) -{ 2 }-> 1 + 1 :|: z = 1 ACTIVATE(z) -{ 2 }-> 1 + 0 :|: z = 1 ACTIVATE(z) -{ 2 }-> 1 + 0 :|: z = 0 ACTIVATE(z) -{ 2 }-> 1 + 0 :|: z - 1 >= 0, z - 1 = z0', z0' >= 0 ADX(z) -{ 1 }-> 0 :|: z >= 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 HD(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 0 :|: z >= 0 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 -{ 2 }-> 1 + ADX(1) + 1 :|: NATS -{ 2 }-> 1 + ADX(1) + 0 :|: NATS -{ 2 }-> 1 + ADX(0) + 1 :|: NATS -{ 2 }-> 1 + ADX(0) + 0 :|: NATS -{ 2 }-> 1 + ADX(1 + 0 + 1) + 1 :|: NATS -{ 2 }-> 1 + ADX(1 + 0 + 1) + 0 :|: S(z) -{ 1 }-> 0 :|: z >= 0 TL(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ZEROS -{ 1 }-> 1 :|: ZEROS -{ 1 }-> 0 :|: activate(z) -{ 0 }-> z :|: z >= 0 activate(z) -{ 0 }-> incr(z - 1) :|: z - 1 >= 0 activate(z) -{ 0 }-> adx(z - 1) :|: z - 1 >= 0 activate(z) -{ 0 }-> 1 :|: z = 1 activate(z) -{ 0 }-> 0 :|: z >= 0 activate(z) -{ 0 }-> 0 :|: z = 1 activate(z) -{ 0 }-> 0 :|: z = 0 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 hd(z) -{ 0 }-> activate(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 hd(z) -{ 0 }-> 0 :|: 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 nats -{ 0 }-> adx(1) :|: nats -{ 0 }-> adx(0) :|: nats -{ 0 }-> adx(1 + 0 + 1) :|: nats -{ 0 }-> 0 :|: s(z) -{ 0 }-> 0 :|: z >= 0 s(z) -{ 0 }-> 1 + z :|: z >= 0 tl(z) -{ 0 }-> activate(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 tl(z) -{ 0 }-> 0 :|: z >= 0 zeros -{ 0 }-> 1 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: ---------------------------------------- (27) 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] zeros -> null_zeros [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] hd(v0) -> null_hd [0] tl(v0) -> null_tl [0] 0'' -> null_0'' [0] s(v0) -> null_s [0] activate(v0) -> null_activate [0] HD(v0) -> null_HD [0] TL(v0) -> null_TL [0] And the following fresh constants: null_nats, null_zeros, null_incr, null_adx, null_hd, null_tl, null_0'', null_s, null_activate, null_HD, null_TL, const ---------------------------------------- (28) 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 -> c(ADX(zeros), ZEROS) [1] ZEROS -> c1 [1] ZEROS -> c2 [1] INCR(cons(z0, z1)) -> c3(ACTIVATE(z0)) [1] INCR(cons(z0, z1)) -> c4(ACTIVATE(z1)) [1] INCR(z0) -> c5 [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] ADX(z0) -> c8 [1] HD(cons(z0, z1)) -> c9(ACTIVATE(z0)) [1] TL(cons(z0, z1)) -> c10(ACTIVATE(z1)) [1] 0' -> c11 [1] S(z0) -> c12 [1] ACTIVATE(n__0) -> c13(0') [1] ACTIVATE(n__zeros) -> c14(ZEROS) [1] ACTIVATE(n__s(z0)) -> c15(S(z0)) [1] ACTIVATE(n__incr(z0)) -> c16(INCR(z0)) [1] ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) [1] ACTIVATE(z0) -> c18 [1] nats -> adx(zeros) [0] zeros -> cons(n__0, n__zeros) [0] zeros -> n__zeros [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] hd(cons(z0, z1)) -> activate(z0) [0] tl(cons(z0, z1)) -> activate(z1) [0] 0'' -> n__0 [0] s(z0) -> n__s(z0) [0] activate(n__0) -> 0'' [0] activate(n__zeros) -> zeros [0] activate(n__s(z0)) -> s(z0) [0] activate(n__incr(z0)) -> incr(z0) [0] activate(n__adx(z0)) -> adx(z0) [0] activate(z0) -> z0 [0] nats -> null_nats [0] zeros -> null_zeros [0] incr(v0) -> null_incr [0] adx(v0) -> null_adx [0] hd(v0) -> null_hd [0] tl(v0) -> null_tl [0] 0'' -> null_0'' [0] s(v0) -> null_s [0] activate(v0) -> null_activate [0] HD(v0) -> null_HD [0] TL(v0) -> null_TL [0] The TRS has the following type information: NATS :: c c :: c6:c7:c8 -> c1:c2 -> c ADX :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c6:c7:c8 zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate ZEROS :: c1:c2 c1 :: c1:c2 c2 :: c1:c2 INCR :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c3:c4:c5 cons :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c3 :: c13:c14:c15:c16:c17:c18 -> c3:c4:c5 ACTIVATE :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> 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:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate n__adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c7 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 -> c6:c7:c8 c8 :: c6:c7:c8 HD :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c9:null_HD c9 :: c13:c14:c15:c16:c17:c18 -> c9:null_HD TL :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c10:null_TL c10 :: c13:c14:c15:c16:c17:c18 -> c10:null_TL 0' :: c11 c11 :: c11 S :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> c12 c12 :: c12 n__0 :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c13 :: c11 -> c13:c14:c15:c16:c17:c18 n__zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c14 :: c1:c2 -> c13:c14:c15:c16:c17:c18 n__s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c15 :: c12 -> c13:c14:c15:c16:c17:c18 n__incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate c16 :: c3:c4:c5 -> c13:c14:c15:c16:c17:c18 c17 :: c6:c7:c8 -> c13:c14:c15:c16:c17:c18 c18 :: c13:c14:c15:c16:c17:c18 nats :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate hd :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate tl :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate 0'' :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate -> cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_nats :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_zeros :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_incr :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_adx :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_hd :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_tl :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_0'' :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_s :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_activate :: cons:n__adx:n__0:n__zeros:n__s:n__incr:null_nats:null_zeros:null_incr:null_adx:null_hd:null_tl:null_0'':null_s:null_activate null_HD :: c9:null_HD null_TL :: c10:null_TL const :: c Rewrite Strategy: INNERMOST ---------------------------------------- (29) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: c1 => 0 c2 => 1 c5 => 0 c8 => 0 c11 => 0 c12 => 0 n__0 => 0 n__zeros => 1 c18 => 0 null_nats => 0 null_zeros => 0 null_incr => 0 null_adx => 0 null_hd => 0 null_tl => 0 null_0'' => 0 null_s => 0 null_activate => 0 null_HD => 0 null_TL => 0 const => 0 ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: 0' -{ 1 }-> 0 :|: 0'' -{ 0 }-> 0 :|: ACTIVATE(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ZEROS :|: z = 1 ACTIVATE(z) -{ 1 }-> 1 + S(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + INCR(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + ADX(z0) :|: z = 1 + z0, z0 >= 0 ACTIVATE(z) -{ 1 }-> 1 + 0' :|: z = 0 ADX(z) -{ 1 }-> 0 :|: z = 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 HD(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 HD(z) -{ 1 }-> 1 + ACTIVATE(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 INCR(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 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 -{ 1 }-> 1 + ADX(zeros) + ZEROS :|: S(z) -{ 1 }-> 0 :|: z = z0, z0 >= 0 TL(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 TL(z) -{ 1 }-> 1 + ACTIVATE(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ZEROS -{ 1 }-> 1 :|: ZEROS -{ 1 }-> 0 :|: 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 }-> adx(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 hd(z) -{ 0 }-> activate(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 hd(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 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 nats -{ 0 }-> adx(zeros) :|: nats -{ 0 }-> 0 :|: s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 s(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 tl(z) -{ 0 }-> activate(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 tl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 zeros -{ 0 }-> 1 :|: zeros -{ 0 }-> 0 :|: zeros -{ 0 }-> 1 + 0 + 1 :|: Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (31) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (32) 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(z0) activate(n__adx(z0)) -> adx(z0) activate(z0) -> z0 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) ACTIVATE(z0) -> c18 Tuples: NATS' -> c19(ADX'(zeros), ZEROS') ZEROS' -> c20 ZEROS' -> c21 INCR'(cons(z0, z1)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) INCR'(z0) -> c23 ADX'(cons(z0, z1)) -> c24(INCR'(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1)) ADX'(z0) -> c25 HD'(cons(z0, z1)) -> c26(ACTIVATE'(z0)) TL'(cons(z0, z1)) -> c27(ACTIVATE'(z1)) 0'' -> c28 S'(z0) -> c29 ACTIVATE'(n__0) -> c30(0'') ACTIVATE'(n__zeros) -> c31(ZEROS') ACTIVATE'(n__s(z0)) -> c32(S'(z0)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) ACTIVATE'(z0) -> c35 NATS'' -> c36(ADX''(zeros), ZEROS', ZEROS'') ZEROS'' -> c37 ZEROS'' -> c38 INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) INCR''(z0) -> c41 ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ADX''(z0) -> c44 HD''(cons(z0, z1)) -> c45(ACTIVATE''(z0)) TL''(cons(z0, z1)) -> c46(ACTIVATE''(z1)) 0''' -> c47 S''(z0) -> c48 ACTIVATE''(n__0) -> c49(0''') ACTIVATE''(n__zeros) -> c50(ZEROS'') ACTIVATE''(n__s(z0)) -> c51(S''(z0)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ACTIVATE''(z0) -> c54 S tuples: NATS'' -> c36(ADX''(zeros), ZEROS', ZEROS'') ZEROS'' -> c37 ZEROS'' -> c38 INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) INCR''(z0) -> c41 ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ADX''(z0) -> c44 HD''(cons(z0, z1)) -> c45(ACTIVATE''(z0)) TL''(cons(z0, z1)) -> c46(ACTIVATE''(z1)) 0''' -> c47 S''(z0) -> c48 ACTIVATE''(n__0) -> c49(0''') ACTIVATE''(n__zeros) -> c50(ZEROS'') ACTIVATE''(n__s(z0)) -> c51(S''(z0)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ACTIVATE''(z0) -> c54 K tuples:none Defined Rule Symbols: NATS, ZEROS, INCR_1, ADX_1, HD_1, TL_1, 0', S_1, ACTIVATE_1, 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, NATS'', ZEROS'', INCR''_1, ADX''_1, HD''_1, TL''_1, 0''', S''_1, ACTIVATE''_1 Compound Symbols: c19_2, c20, c21, c22_2, c23, c24_3, c25, c26_1, c27_1, c28, c29, c30_1, c31_1, c32_1, c33_1, c34_1, c35, c36_3, c37, c38, c39_1, c40_1, c41, c42_4, c43_4, c44, c45_1, c46_1, c47, c48, c49_1, c50_1, c51_1, c52_1, c53_1, c54 ---------------------------------------- (33) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 4 leading nodes: HD'(cons(z0, z1)) -> c26(ACTIVATE'(z0)) TL'(cons(z0, z1)) -> c27(ACTIVATE'(z1)) HD''(cons(z0, z1)) -> c45(ACTIVATE''(z0)) TL''(cons(z0, z1)) -> c46(ACTIVATE''(z1)) Removed 20 trailing nodes: S''(z0) -> c48 ACTIVATE''(n__s(z0)) -> c51(S''(z0)) ZEROS' -> c20 ACTIVATE'(n__s(z0)) -> c32(S'(z0)) ACTIVATE'(z0) -> c35 ACTIVATE''(n__0) -> c49(0''') INCR''(z0) -> c41 INCR'(z0) -> c23 ZEROS'' -> c37 ACTIVATE'(n__0) -> c30(0'') ACTIVATE''(n__zeros) -> c50(ZEROS'') ADX''(z0) -> c44 ZEROS'' -> c38 0''' -> c47 0'' -> c28 ADX'(z0) -> c25 S'(z0) -> c29 ACTIVATE'(n__zeros) -> c31(ZEROS') ACTIVATE''(z0) -> c54 ZEROS' -> c21 ---------------------------------------- (34) 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(z0) activate(n__adx(z0)) -> adx(z0) activate(z0) -> z0 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) ACTIVATE(z0) -> c18 Tuples: NATS' -> c19(ADX'(zeros), ZEROS') INCR'(cons(z0, z1)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ADX'(cons(z0, z1)) -> c24(INCR'(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) NATS'' -> c36(ADX''(zeros), ZEROS', ZEROS'') INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) S tuples: NATS'' -> c36(ADX''(zeros), ZEROS', ZEROS'') INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) K tuples:none Defined Rule Symbols: NATS, ZEROS, INCR_1, ADX_1, HD_1, TL_1, 0', S_1, ACTIVATE_1, 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, NATS'', INCR''_1, ADX''_1, ACTIVATE''_1 Compound Symbols: c19_2, c22_2, c24_3, c33_1, c34_1, c36_3, c39_1, c40_1, c42_4, c43_4, c52_1, c53_1 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (36) 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(z0) activate(n__adx(z0)) -> adx(z0) activate(z0) -> z0 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) ACTIVATE(z0) -> c18 Tuples: INCR'(cons(z0, z1)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ADX'(cons(z0, z1)) -> c24(INCR'(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS'' -> c36(ADX''(zeros)) K tuples:none Defined Rule Symbols: NATS, ZEROS, INCR_1, ADX_1, HD_1, TL_1, 0', S_1, ACTIVATE_1, nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1 Defined Pair Symbols: INCR'_1, ADX'_1, ACTIVATE'_1, INCR''_1, ADX''_1, ACTIVATE''_1, NATS', NATS'' Compound Symbols: c22_2, c24_3, c33_1, c34_1, c39_1, c40_1, c42_4, c43_4, c52_1, c53_1, c19_1, c36_1 ---------------------------------------- (37) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: NATS'' -> c36(ADX''(zeros)) ---------------------------------------- (38) 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(z0) activate(n__adx(z0)) -> adx(z0) activate(z0) -> z0 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) ACTIVATE(z0) -> c18 Tuples: INCR'(cons(z0, z1)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ADX'(cons(z0, z1)) -> c24(INCR'(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: NATS, ZEROS, INCR_1, ADX_1, HD_1, TL_1, 0', S_1, ACTIVATE_1, nats, zeros, incr_1, adx_1, hd_1, tl_1, 0, s_1, activate_1 Defined Pair Symbols: INCR'_1, ADX'_1, ACTIVATE'_1, INCR''_1, ADX''_1, ACTIVATE''_1, NATS', NATS'' Compound Symbols: c22_2, c24_3, c33_1, c34_1, c39_1, c40_1, c42_4, c43_4, c52_1, c53_1, c19_1, c36_1 ---------------------------------------- (39) 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) 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(z0)) ACTIVATE(n__adx(z0)) -> c17(ADX(z0)) ACTIVATE(z0) -> c18 ---------------------------------------- (40) 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ADX'(cons(z0, z1)) -> c24(INCR'(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ADX'_1, ACTIVATE'_1, INCR''_1, ADX''_1, ACTIVATE''_1, NATS', NATS'' Compound Symbols: c22_2, c24_3, c33_1, c34_1, c39_1, c40_1, c42_4, c43_4, c52_1, c53_1, c19_1, c36_1 ---------------------------------------- (41) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(z0, z1)) -> c24(INCR'(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1)) by ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(n__0), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ---------------------------------------- (42) 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(n__0), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ADX''_1, ACTIVATE''_1, NATS', NATS'', ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c42_4, c43_4, c52_1, c53_1, c19_1, c36_1, c24_3 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (44) 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ADX''_1, ACTIVATE''_1, NATS', NATS'', ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c42_4, c43_4, c52_1, c53_1, c19_1, c36_1, c24_3, c24_2 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(z0, z1)) -> c42(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z0)) by ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(n__0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ---------------------------------------- (46) 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(n__0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(n__0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ADX''_1, ACTIVATE''_1, NATS', NATS'', ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c43_4, c52_1, c53_1, c19_1, c36_1, c24_3, c24_2, c42_4 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 9 trailing tuple parts ---------------------------------------- (48) 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ADX''_1, ACTIVATE''_1, NATS', NATS'', ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c43_4, c52_1, c53_1, c19_1, c36_1, c24_3, c24_2, c42_4, c42_3, c42_2 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(z0, z1)) -> c43(INCR''(cons(activate(z0), n__adx(activate(z1)))), ACTIVATE'(z0), ACTIVATE'(z1), ACTIVATE''(z1)) by ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ---------------------------------------- (50) 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, NATS', NATS'', ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c19_1, c36_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 9 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS' -> c19(ADX'(zeros)) NATS'' -> c36(ADX''(zeros)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, NATS', NATS'', ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c19_1, c36_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace NATS' -> c19(ADX'(zeros)) by NATS' -> c19(ADX'(cons(n__0, n__zeros))) NATS' -> c19(ADX'(n__zeros)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS'' -> c36(ADX''(zeros)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) NATS' -> c19(ADX'(cons(n__0, n__zeros))) NATS' -> c19(ADX'(n__zeros)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, NATS'', ADX'_1, ADX''_1, NATS' Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c36_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c19_1 ---------------------------------------- (55) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: NATS' -> c19(ADX'(cons(n__0, n__zeros))) Removed 1 trailing nodes: NATS' -> c19(ADX'(n__zeros)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) NATS'' -> c36(ADX''(zeros)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, NATS'', ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c36_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace NATS'' -> c36(ADX''(zeros)) by NATS'' -> c36(ADX''(cons(n__0, n__zeros))) NATS'' -> c36(ADX''(n__zeros)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) NATS'' -> c36(ADX''(cons(n__0, n__zeros))) NATS'' -> c36(ADX''(n__zeros)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) K tuples: NATS'' -> c36(ADX''(zeros)) Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1, NATS'' Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c36_1 ---------------------------------------- (59) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: NATS'' -> c36(ADX''(cons(n__0, n__zeros))) Removed 1 trailing nodes: NATS'' -> c36(ADX''(n__zeros)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) by ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) by ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(x0, z0)) -> c24(INCR'(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) by ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(n__0), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(n__zeros), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(n__0), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(n__zeros), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) by ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__0)) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__zeros)) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__s(z0))) ADX'(cons(n__incr(x0), n__incr(z0))) -> c24(INCR'(cons(incr(x0), n__adx(incr(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(x0), n__adx(z0))) -> c24(INCR'(cons(incr(x0), n__adx(adx(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(x0), z0)) -> c24(INCR'(cons(incr(x0), n__adx(z0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(z0)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__0)) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__zeros)) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__s(z0))) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) by ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__0)) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__zeros)) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__s(z0))) ADX'(cons(n__adx(x0), n__incr(z0))) -> c24(INCR'(cons(adx(x0), n__adx(incr(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__incr(z0))) ADX'(cons(n__adx(x0), n__adx(z0))) -> c24(INCR'(cons(adx(x0), n__adx(adx(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__adx(z0))) ADX'(cons(n__adx(x0), z0)) -> c24(INCR'(cons(adx(x0), n__adx(z0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(z0)) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__0)) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__zeros)) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__s(z0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_3, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1)) by ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(x0, n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(x0, n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(x0, z0)) -> c24(INCR'(cons(x0, n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) by ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0))), ACTIVATE'(n__zeros)) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0))), ACTIVATE'(n__s(z0))) ADX'(cons(n__incr(z0), n__0)) -> c24(INCR'(cons(incr(z0), n__adx(0))), ACTIVATE'(n__incr(z0))) ADX'(cons(n__adx(z0), n__0)) -> c24(INCR'(cons(adx(z0), n__adx(0))), ACTIVATE'(n__adx(z0))) ADX'(cons(z0, n__0)) -> c24(INCR'(cons(z0, n__adx(0))), ACTIVATE'(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0))), ACTIVATE'(n__zeros)) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0))), ACTIVATE'(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) by ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros))), ACTIVATE'(n__0)) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros))), ACTIVATE'(n__s(z0))) ADX'(cons(n__incr(z0), n__zeros)) -> c24(INCR'(cons(incr(z0), n__adx(zeros))), ACTIVATE'(n__incr(z0))) ADX'(cons(n__adx(z0), n__zeros)) -> c24(INCR'(cons(adx(z0), n__adx(zeros))), ACTIVATE'(n__adx(z0))) ADX'(cons(z0, n__zeros)) -> c24(INCR'(cons(z0, n__adx(zeros))), ACTIVATE'(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros))), ACTIVATE'(n__0)) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros))), ACTIVATE'(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) by ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1)))), ACTIVATE'(n__0)) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1)))), ACTIVATE'(n__zeros)) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1)))), ACTIVATE'(n__s(z0))) ADX'(cons(n__incr(z0), n__s(x1))) -> c24(INCR'(cons(incr(z0), n__adx(s(x1)))), ACTIVATE'(n__incr(z0))) ADX'(cons(n__adx(z0), n__s(x1))) -> c24(INCR'(cons(adx(z0), n__adx(s(x1)))), ACTIVATE'(n__adx(z0))) ADX'(cons(z0, n__s(x1))) -> c24(INCR'(cons(z0, n__adx(s(x1)))), ACTIVATE'(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1)))), ACTIVATE'(n__0)) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1)))), ACTIVATE'(n__zeros)) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1)))), ACTIVATE'(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) by ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX'(cons(n__0, n__s(z0))) -> c24(INCR'(cons(0, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX'(cons(n__0, n__incr(z0))) -> c24(INCR'(cons(0, n__adx(incr(z0)))), ACTIVATE'(n__incr(z0))) ADX'(cons(n__0, n__adx(z0))) -> c24(INCR'(cons(0, n__adx(adx(z0)))), ACTIVATE'(n__adx(z0))) ADX'(cons(n__0, z0)) -> c24(INCR'(cons(0, n__adx(z0))), ACTIVATE'(z0)) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX'(cons(n__0, n__s(z0))) -> c24(INCR'(cons(0, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) by ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0))), ACTIVATE'(n__0)) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX'(cons(n__zeros, n__s(z0))) -> c24(INCR'(cons(zeros, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX'(cons(n__zeros, n__incr(z0))) -> c24(INCR'(cons(zeros, n__adx(incr(z0)))), ACTIVATE'(n__incr(z0))) ADX'(cons(n__zeros, n__adx(z0))) -> c24(INCR'(cons(zeros, n__adx(adx(z0)))), ACTIVATE'(n__adx(z0))) ADX'(cons(n__zeros, z0)) -> c24(INCR'(cons(zeros, n__adx(z0))), ACTIVATE'(z0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0))), ACTIVATE'(n__0)) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX'(cons(n__zeros, n__s(z0))) -> c24(INCR'(cons(zeros, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX'_1, ADX''_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c24_2, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) by ADX'(cons(n__s(x0), n__0)) -> c24(INCR'(cons(s(x0), n__adx(0))), ACTIVATE'(n__0)) ADX'(cons(n__s(x0), n__zeros)) -> c24(INCR'(cons(s(x0), n__adx(zeros))), ACTIVATE'(n__zeros)) ADX'(cons(n__s(x0), n__s(z0))) -> c24(INCR'(cons(s(x0), n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX'(cons(n__s(x0), n__incr(z0))) -> c24(INCR'(cons(s(x0), n__adx(incr(z0)))), ACTIVATE'(n__incr(z0))) ADX'(cons(n__s(x0), n__adx(z0))) -> c24(INCR'(cons(s(x0), n__adx(adx(z0)))), ACTIVATE'(n__adx(z0))) ADX'(cons(n__s(x0), z0)) -> c24(INCR'(cons(s(x0), n__adx(z0))), ACTIVATE'(z0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(x0), n__0)) -> c24(INCR'(cons(s(x0), n__adx(0))), ACTIVATE'(n__0)) ADX'(cons(n__s(x0), n__zeros)) -> c24(INCR'(cons(s(x0), n__adx(zeros))), ACTIVATE'(n__zeros)) ADX'(cons(n__s(x0), n__s(z0))) -> c24(INCR'(cons(s(x0), n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) by ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), 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, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) by ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, z0)) -> c42(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) by ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(n__0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(n__0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(n__0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) by ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__0), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__incr(z0))) -> c42(INCR''(cons(incr(x0), n__adx(incr(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__adx(z0))) -> c42(INCR''(cons(incr(x0), n__adx(adx(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), z0)) -> c42(INCR''(cons(incr(x0), n__adx(z0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(z0), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__0), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__0), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), 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, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) by ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__0), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__incr(z0))) -> c42(INCR''(cons(adx(x0), n__adx(incr(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__adx(z0))) -> c42(INCR''(cons(adx(x0), n__adx(adx(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), z0)) -> c42(INCR''(cons(adx(x0), n__adx(z0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(z0), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__0), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__0), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), 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, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_4, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) by ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(x0, n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(x0, n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(x0, z0)) -> c42(INCR''(cons(x0, n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(x0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(x0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4 ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) by ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0))), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__0)) -> c42(INCR''(cons(incr(z0), n__adx(0))), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__0)) -> c42(INCR''(cons(adx(z0), n__adx(0))), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__0)) -> c42(INCR''(cons(z0, n__adx(0))), ACTIVATE'(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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0))), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0))), ACTIVATE'(n__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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) by ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros))), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__zeros)) -> c42(INCR''(cons(incr(z0), n__adx(zeros))), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__zeros)) -> c42(INCR''(cons(adx(z0), n__adx(zeros))), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__zeros)) -> c42(INCR''(cons(z0, n__adx(zeros))), ACTIVATE'(z0), ACTIVATE''(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros))), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros))), ACTIVATE'(n__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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_3, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) by ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1)))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1)))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(z0), n__s(x1))) -> c42(INCR''(cons(incr(z0), n__adx(s(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__s(x1))) -> c42(INCR''(cons(adx(z0), n__adx(s(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__s(x1))) -> c42(INCR''(cons(z0, n__adx(s(x1)))), ACTIVATE'(z0), ACTIVATE''(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1)))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1)))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1)))), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1)))), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1)))), ACTIVATE'(n__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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_3, c42_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_3, c42_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1)) by ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__0, n__s(z0))) -> c42(INCR''(cons(0, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__0, n__incr(z0))) -> c42(INCR''(cons(0, n__adx(incr(z0)))), ACTIVATE'(n__incr(z0))) ADX''(cons(n__0, n__adx(z0))) -> c42(INCR''(cons(0, n__adx(adx(z0)))), ACTIVATE'(n__adx(z0))) ADX''(cons(n__0, z0)) -> c42(INCR''(cons(0, n__adx(z0))), ACTIVATE'(z0)) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__0, n__s(z0))) -> c42(INCR''(cons(0, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__0, n__s(z0))) -> c42(INCR''(cons(0, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__0, x0)) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_3, c42_1 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_3, c42_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1)) by ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__zeros, n__s(z0))) -> c42(INCR''(cons(zeros, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__zeros, n__incr(z0))) -> c42(INCR''(cons(zeros, n__adx(incr(z0)))), ACTIVATE'(n__incr(z0))) ADX''(cons(n__zeros, n__adx(z0))) -> c42(INCR''(cons(zeros, n__adx(adx(z0)))), ACTIVATE'(n__adx(z0))) ADX''(cons(n__zeros, z0)) -> c42(INCR''(cons(zeros, n__adx(z0))), ACTIVATE'(z0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__zeros, n__s(z0))) -> c42(INCR''(cons(zeros, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__zeros, n__s(z0))) -> c42(INCR''(cons(zeros, n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_3, c42_1 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c42_2, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_3, c42_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) by ADX''(cons(n__s(x0), n__0)) -> c42(INCR''(cons(s(x0), n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__s(x0), n__zeros)) -> c42(INCR''(cons(s(x0), n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__s(x0), n__s(z0))) -> c42(INCR''(cons(s(x0), n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__s(x0), n__incr(z0))) -> c42(INCR''(cons(s(x0), n__adx(incr(z0)))), ACTIVATE'(n__incr(z0))) ADX''(cons(n__s(x0), n__adx(z0))) -> c42(INCR''(cons(s(x0), n__adx(adx(z0)))), ACTIVATE'(n__adx(z0))) ADX''(cons(n__s(x0), z0)) -> c42(INCR''(cons(s(x0), n__adx(z0))), ACTIVATE'(z0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(x0), n__0)) -> c42(INCR''(cons(s(x0), n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__s(x0), n__zeros)) -> c42(INCR''(cons(s(x0), n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__s(x0), n__s(z0))) -> c42(INCR''(cons(s(x0), n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(x0), n__0)) -> c42(INCR''(cons(s(x0), n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__s(x0), n__zeros)) -> c42(INCR''(cons(s(x0), n__adx(zeros))), ACTIVATE'(n__zeros)) ADX''(cons(n__s(x0), n__s(z0))) -> c42(INCR''(cons(s(x0), n__adx(s(z0)))), ACTIVATE'(n__s(z0))) ADX''(cons(n__s(z0), x1)) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) by ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) by ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__zeros), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__s(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, z0)) -> c43(INCR''(cons(activate(x0), n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) by ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(n__0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(n__zeros), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(n__s(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) by ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(x0), n__incr(z0))) -> c43(INCR''(cons(incr(x0), n__adx(incr(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__adx(z0))) -> c43(INCR''(cons(incr(x0), n__adx(adx(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(x0), z0)) -> c43(INCR''(cons(incr(x0), n__adx(z0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), 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, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) by ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__adx(x0), n__incr(z0))) -> c43(INCR''(cons(adx(x0), n__adx(incr(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(x0), n__adx(z0))) -> c43(INCR''(cons(adx(x0), n__adx(adx(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), z0)) -> c43(INCR''(cons(adx(x0), n__adx(z0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(z0), ACTIVATE''(z0)) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), 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, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_4, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(activate(x1)))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) by ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(x0, n__adx(incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(x0, n__adx(adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(x0, z0)) -> c43(INCR''(cons(x0, n__adx(z0))), ACTIVATE'(x0), ACTIVATE'(z0), ACTIVATE''(z0)) ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__s(z0)), ACTIVATE''(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE'(n__0), ACTIVATE''(n__0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE'(n__zeros), ACTIVATE''(n__zeros)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE'(n__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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1, c43_4 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) K tuples:none Defined Rule Symbols: activate_1, 0, zeros, s_1, incr_1, adx_1 Defined Pair Symbols: INCR'_1, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1, c43_4 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(0))), ACTIVATE'(x0)) by ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX''(cons(n__0, n__0)) -> c43(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__zeros, n__0)) -> c43(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__zeros)) ADX''(cons(n__s(z0), n__0)) -> c43(INCR''(cons(s(z0), n__adx(0))), ACTIVATE'(n__s(z0))) ADX''(cons(n__incr(z0), n__0)) -> c43(INCR''(cons(incr(z0), n__adx(0))), ACTIVATE'(n__incr(z0))) ADX''(cons(n__adx(z0), n__0)) -> c43(INCR''(cons(adx(z0), n__adx(0))), ACTIVATE'(n__adx(z0))) ADX''(cons(z0, n__0)) -> c43(INCR''(cons(z0, n__adx(0))), ACTIVATE'(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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX''(cons(n__0, n__0)) -> c43(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__zeros, n__0)) -> c43(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__zeros)) ADX''(cons(n__s(z0), n__0)) -> c43(INCR''(cons(s(z0), n__adx(0))), ACTIVATE'(n__s(z0))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX''(cons(n__0, n__0)) -> c43(INCR''(cons(0, n__adx(0))), ACTIVATE'(n__0)) ADX''(cons(n__zeros, n__0)) -> c43(INCR''(cons(zeros, n__adx(0))), ACTIVATE'(n__zeros)) ADX''(cons(n__s(z0), n__0)) -> c43(INCR''(cons(s(z0), n__adx(0))), 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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1, c43_4 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(z0) activate(n__adx(z0)) -> adx(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)) -> c22(ACTIVATE'(z0), ACTIVATE'(z1)) ACTIVATE'(n__incr(z0)) -> c33(INCR'(z0)) ACTIVATE'(n__adx(z0)) -> c34(ADX'(z0)) INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX'(cons(x0, n__incr(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1)))) ADX'(cons(x0, n__incr(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0))) ADX'(cons(n__incr(z0), n__incr(x1))) -> c24(INCR'(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(n__adx(z0), n__incr(x1))) -> c24(INCR'(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1))) ADX'(cons(z0, n__incr(x1))) -> c24(INCR'(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1))) ADX'(cons(n__0, n__incr(x1))) -> c24(INCR'(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__zeros, n__incr(x1))) -> c24(INCR'(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(n__s(z0), n__incr(x1))) -> c24(INCR'(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX'(cons(x0, n__adx(cons(z0, z1)))) -> c24(INCR'(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1)))) ADX'(cons(x0, n__adx(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0))) ADX'(cons(n__incr(z0), n__adx(x1))) -> c24(INCR'(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(n__adx(z0), n__adx(x1))) -> c24(INCR'(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1))) ADX'(cons(z0, n__adx(x1))) -> c24(INCR'(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1))) ADX'(cons(n__0, n__adx(x1))) -> c24(INCR'(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__zeros, n__adx(x1))) -> c24(INCR'(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__s(z0), n__adx(x1))) -> c24(INCR'(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(z0, x1)) -> c24(INCR'(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1)) ADX'(cons(n__0, x1)) -> c24(INCR'(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__zeros, x1)) -> c24(INCR'(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX'(cons(n__incr(cons(z0, z1)), x1)) -> c24(INCR'(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__incr(z0), x1)) -> c24(INCR'(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1)) ADX'(cons(n__incr(x0), n__0)) -> c24(INCR'(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__zeros)) -> c24(INCR'(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__incr(x0), n__s(z0))) -> c24(INCR'(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX'(cons(n__adx(cons(z0, z1)), x1)) -> c24(INCR'(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1)) ADX'(cons(n__adx(z0), x1)) -> c24(INCR'(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1)) ADX'(cons(n__adx(x0), n__0)) -> c24(INCR'(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__zeros)) -> c24(INCR'(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX'(cons(n__adx(x0), n__s(z0))) -> c24(INCR'(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX'(cons(x0, n__0)) -> c24(INCR'(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX'(cons(n__0, n__0)) -> c24(INCR'(cons(0, n__adx(0)))) ADX'(cons(n__zeros, n__0)) -> c24(INCR'(cons(zeros, n__adx(0)))) ADX'(cons(n__s(z0), n__0)) -> c24(INCR'(cons(s(z0), n__adx(0)))) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0)) ADX'(cons(x0, n__zeros)) -> c24(INCR'(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0)) ADX'(cons(n__0, n__zeros)) -> c24(INCR'(cons(0, n__adx(zeros)))) ADX'(cons(n__zeros, n__zeros)) -> c24(INCR'(cons(zeros, n__adx(zeros)))) ADX'(cons(n__s(z0), n__zeros)) -> c24(INCR'(cons(s(z0), n__adx(zeros)))) ADX'(cons(x0, n__s(z0))) -> c24(INCR'(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0)) ADX'(cons(n__0, n__s(x1))) -> c24(INCR'(cons(0, n__adx(s(x1))))) ADX'(cons(n__zeros, n__s(x1))) -> c24(INCR'(cons(zeros, n__adx(s(x1))))) ADX'(cons(n__s(z0), n__s(x1))) -> c24(INCR'(cons(s(z0), n__adx(s(x1))))) ADX'(cons(n__0, x0)) -> c24(INCR'(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__zeros, x0)) -> c24(INCR'(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX'(cons(n__s(z0), x1)) -> c24(INCR'(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX''(cons(n__0, n__0)) -> c43(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c43(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c43(INCR''(cons(s(z0), n__adx(0)))) S tuples: INCR''(cons(z0, z1)) -> c39(ACTIVATE''(z0)) INCR''(cons(z0, z1)) -> c40(ACTIVATE''(z1)) ACTIVATE''(n__incr(z0)) -> c52(INCR''(z0)) ACTIVATE''(n__adx(z0)) -> c53(ADX''(z0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(activate(x0), n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(activate(x0), n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(activate(x1)))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__incr(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__incr(x1))) -> c42(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c42(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__incr(x1))) -> c42(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__incr(x1))) -> c42(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c42(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c42(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c42(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(x0)) ADX''(cons(x0, n__adx(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(x0)) ADX''(cons(n__incr(z0), n__adx(x1))) -> c42(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c42(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, n__adx(x1))) -> c42(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(z0)) ADX''(cons(n__0, n__adx(x1))) -> c42(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c42(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c42(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(z0, x1)) -> c42(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(z0)) ADX''(cons(n__0, x1)) -> c42(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__zeros, x1)) -> c42(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c42(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(n__incr(z0), x1)) -> c42(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(x0), n__0)) -> c42(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c42(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c42(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0)), ACTIVATE''(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c42(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(n__adx(z0), x1)) -> c42(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(n__adx(z0))) ADX''(cons(n__adx(x0), n__0)) -> c42(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c42(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c42(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0)), ACTIVATE''(n__adx(x0))) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__0)) -> c42(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__0)) -> c42(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c42(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c42(INCR''(cons(s(z0), n__adx(0)))) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(cons(n__0, n__zeros)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(x0, n__zeros)) -> c42(INCR''(cons(activate(x0), n__adx(n__zeros))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__zeros)) -> c42(INCR''(cons(0, n__adx(zeros)))) ADX''(cons(n__zeros, n__zeros)) -> c42(INCR''(cons(zeros, n__adx(zeros)))) ADX''(cons(n__s(z0), n__zeros)) -> c42(INCR''(cons(s(z0), n__adx(zeros)))) ADX''(cons(x0, n__s(z0))) -> c42(INCR''(cons(activate(x0), n__adx(n__s(z0)))), ACTIVATE'(x0), ACTIVATE''(x0)) ADX''(cons(n__0, n__s(x1))) -> c42(INCR''(cons(0, n__adx(s(x1))))) ADX''(cons(n__zeros, n__s(x1))) -> c42(INCR''(cons(zeros, n__adx(s(x1))))) ADX''(cons(n__s(z0), n__s(x1))) -> c42(INCR''(cons(s(z0), n__adx(s(x1))))) ADX''(cons(n__0, x0)) -> c42(INCR''(cons(n__0, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(cons(n__0, n__zeros), n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__zeros, x0)) -> c42(INCR''(cons(n__zeros, n__adx(activate(x0)))), ACTIVATE'(x0)) ADX''(cons(n__s(z0), x1)) -> c42(INCR''(cons(n__s(z0), n__adx(activate(x1)))), ACTIVATE'(x1)) ADX''(cons(x0, n__incr(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(cons(n__s(activate(z0)), n__incr(activate(z1)))))), ACTIVATE'(x0), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE''(n__incr(cons(z0, z1)))) ADX''(cons(x0, n__incr(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__incr(z0)))), ACTIVATE'(x0), ACTIVATE'(n__incr(z0)), ACTIVATE''(n__incr(z0))) ADX''(cons(n__incr(z0), n__incr(x1))) -> c43(INCR''(cons(incr(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__adx(z0), n__incr(x1))) -> c43(INCR''(cons(adx(z0), n__adx(incr(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(z0, n__incr(x1))) -> c43(INCR''(cons(z0, n__adx(incr(x1)))), ACTIVATE'(z0), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__0, n__incr(x1))) -> c43(INCR''(cons(0, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__zeros, n__incr(x1))) -> c43(INCR''(cons(zeros, n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(n__s(z0), n__incr(x1))) -> c43(INCR''(cons(s(z0), n__adx(incr(x1)))), ACTIVATE'(n__incr(x1)), ACTIVATE''(n__incr(x1))) ADX''(cons(x0, n__adx(cons(z0, z1)))) -> c43(INCR''(cons(activate(x0), n__adx(incr(cons(activate(z0), n__adx(activate(z1))))))), ACTIVATE'(x0), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE''(n__adx(cons(z0, z1)))) ADX''(cons(x0, n__adx(z0))) -> c43(INCR''(cons(activate(x0), n__adx(n__adx(z0)))), ACTIVATE'(x0), ACTIVATE'(n__adx(z0)), ACTIVATE''(n__adx(z0))) ADX''(cons(n__incr(z0), n__adx(x1))) -> c43(INCR''(cons(incr(z0), n__adx(adx(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__adx(z0), n__adx(x1))) -> c43(INCR''(cons(adx(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(z0, n__adx(x1))) -> c43(INCR''(cons(z0, n__adx(adx(x1)))), ACTIVATE'(z0), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__0, n__adx(x1))) -> c43(INCR''(cons(0, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__zeros, n__adx(x1))) -> c43(INCR''(cons(zeros, n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__s(z0), n__adx(x1))) -> c43(INCR''(cons(s(z0), n__adx(adx(x1)))), ACTIVATE'(n__adx(x1)), ACTIVATE''(n__adx(x1))) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(incr(z0), n__adx(x1))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(adx(z0), n__adx(x1))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(z0, x1)) -> c43(INCR''(cons(z0, n__adx(x1))), ACTIVATE'(z0), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__0, x1)) -> c43(INCR''(cons(0, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__zeros, x1)) -> c43(INCR''(cons(zeros, n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__s(z0), x1)) -> c43(INCR''(cons(s(z0), n__adx(x1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(cons(z0, z1)), x1)) -> c43(INCR''(cons(cons(n__s(activate(z0)), n__incr(activate(z1))), n__adx(activate(x1)))), ACTIVATE'(n__incr(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(z0), x1)) -> c43(INCR''(cons(n__incr(z0), n__adx(activate(x1)))), ACTIVATE'(n__incr(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__incr(x0), n__0)) -> c43(INCR''(cons(incr(x0), n__adx(0))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__zeros)) -> c43(INCR''(cons(incr(x0), n__adx(zeros))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__incr(x0), n__s(z0))) -> c43(INCR''(cons(incr(x0), n__adx(s(z0)))), ACTIVATE'(n__incr(x0))) ADX''(cons(n__adx(cons(z0, z1)), x1)) -> c43(INCR''(cons(incr(cons(activate(z0), n__adx(activate(z1)))), n__adx(activate(x1)))), ACTIVATE'(n__adx(cons(z0, z1))), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(z0), x1)) -> c43(INCR''(cons(n__adx(z0), n__adx(activate(x1)))), ACTIVATE'(n__adx(z0)), ACTIVATE'(x1), ACTIVATE''(x1)) ADX''(cons(n__adx(x0), n__0)) -> c43(INCR''(cons(adx(x0), n__adx(0))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__zeros)) -> c43(INCR''(cons(adx(x0), n__adx(zeros))), ACTIVATE'(n__adx(x0))) ADX''(cons(n__adx(x0), n__s(z0))) -> c43(INCR''(cons(adx(x0), n__adx(s(z0)))), ACTIVATE'(n__adx(x0))) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(x0, n__adx(0))), ACTIVATE'(x0)) ADX''(cons(x0, n__zeros)) -> c43(INCR''(cons(x0, n__adx(zeros))), ACTIVATE'(x0)) ADX''(cons(x0, n__s(z0))) -> c43(INCR''(cons(x0, n__adx(s(z0)))), ACTIVATE'(x0)) ADX''(cons(x0, n__0)) -> c43(INCR''(cons(activate(x0), n__adx(n__0))), ACTIVATE'(x0)) ADX''(cons(n__0, n__0)) -> c43(INCR''(cons(0, n__adx(0)))) ADX''(cons(n__zeros, n__0)) -> c43(INCR''(cons(zeros, n__adx(0)))) ADX''(cons(n__s(z0), n__0)) -> c43(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, ACTIVATE'_1, INCR''_1, ACTIVATE''_1, ADX''_1, ADX'_1 Compound Symbols: c22_2, c33_1, c34_1, c39_1, c40_1, c52_1, c53_1, c43_2, c43_3, c24_3, c24_2, c24_1, c42_4, c42_2, c42_3, c42_1, c43_4, c43_1