KILLED proof of input_HtR9VXv484.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 380 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 1 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 109 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 185 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 152 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 59 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 3 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 3035 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 249 ms] (50) CpxRNTS (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 3259 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 423 ms] (56) CpxRNTS (57) CompletionProof [UPPER BOUND(ID), 0 ms] (58) CpxTypedWeightedCompleteTrs (59) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (60) CpxRNTS (61) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtUsableRulesProof [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) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 41 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 46 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 79 ms] (116) CdtProblem (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRewritingProof [BOTH BOUNDS(ID, ID), 8 ms] (132) CdtProblem (133) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 136 ms] (140) CdtProblem (141) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 104 ms] (142) CdtProblem (143) CdtRewritingProof [BOTH BOUNDS(ID, ID), 5 ms] (144) CdtProblem (145) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 189 ms] (152) CdtProblem (153) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRewritingProof [BOTH BOUNDS(ID, ID), 12 ms] (156) CdtProblem (157) CdtRewritingProof [BOTH BOUNDS(ID, ID), 10 ms] (158) CdtProblem (159) CdtRewritingProof [BOTH BOUNDS(ID, ID), 20 ms] (160) CdtProblem (161) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 42 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 177 ms] (166) CdtProblem (167) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 204 ms] (168) CdtProblem (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 4 ms] (172) CdtProblem (173) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 5 ms] (174) CdtProblem (175) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 14 ms] (186) CdtProblem (187) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (200) CdtProblem (201) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) length(n__nil) -> 0 length(n__cons(X, Y)) -> s(length1(activate(Y))) length1(X) -> length(activate(X)) from(X) -> n__from(X) s(X) -> n__s(X) nil -> n__nil cons(X1, X2) -> n__cons(X1, X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(X) -> X S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) length(n__nil) -> 0' length(n__cons(X, Y)) -> s(length1(activate(Y))) length1(X) -> length(activate(X)) from(X) -> n__from(X) s(X) -> n__s(X) nil -> n__nil cons(X1, X2) -> n__cons(X1, X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(X) -> X S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) length(n__nil) -> 0 length(n__cons(X, Y)) -> s(length1(activate(Y))) length1(X) -> length(activate(X)) from(X) -> n__from(X) s(X) -> n__s(X) nil -> n__nil cons(X1, X2) -> n__cons(X1, X2) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__nil) -> nil activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(X) -> X S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) [1] length(n__nil) -> 0 [1] length(n__cons(X, Y)) -> s(length1(activate(Y))) [1] length1(X) -> length(activate(X)) [1] from(X) -> n__from(X) [1] s(X) -> n__s(X) [1] nil -> n__nil [1] cons(X1, X2) -> n__cons(X1, X2) [1] activate(n__from(X)) -> from(activate(X)) [1] activate(n__s(X)) -> s(activate(X)) [1] activate(n__nil) -> nil [1] activate(n__cons(X1, X2)) -> cons(activate(X1), X2) [1] activate(X) -> X [1] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) [1] length(n__nil) -> 0 [1] length(n__cons(X, Y)) -> s(length1(activate(Y))) [1] length1(X) -> length(activate(X)) [1] from(X) -> n__from(X) [1] s(X) -> n__s(X) [1] nil -> n__nil [1] cons(X1, X2) -> n__cons(X1, X2) [1] activate(n__from(X)) -> from(activate(X)) [1] activate(n__s(X)) -> s(activate(X)) [1] activate(n__nil) -> nil [1] activate(n__cons(X1, X2)) -> cons(activate(X1), X2) [1] activate(X) -> X [1] The TRS has the following type information: from :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons cons :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons n__from :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons n__s :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons length :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons n__nil :: n__s:n__from:n__nil:0:n__cons 0 :: n__s:n__from:n__nil:0:n__cons n__cons :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons s :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons length1 :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons activate :: n__s:n__from:n__nil:0:n__cons -> n__s:n__from:n__nil:0:n__cons nil :: n__s:n__from:n__nil:0:n__cons Rewrite Strategy: INNERMOST ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: activate_1 length1_1 length_1 s_1 from_1 cons_2 nil Due to the following rules being added: length(v0) -> null_length [0] And the following fresh constants: null_length ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) [1] length(n__nil) -> 0 [1] length(n__cons(X, Y)) -> s(length1(activate(Y))) [1] length1(X) -> length(activate(X)) [1] from(X) -> n__from(X) [1] s(X) -> n__s(X) [1] nil -> n__nil [1] cons(X1, X2) -> n__cons(X1, X2) [1] activate(n__from(X)) -> from(activate(X)) [1] activate(n__s(X)) -> s(activate(X)) [1] activate(n__nil) -> nil [1] activate(n__cons(X1, X2)) -> cons(activate(X1), X2) [1] activate(X) -> X [1] length(v0) -> null_length [0] The TRS has the following type information: from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length length :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__nil :: n__s:n__from:n__nil:0:n__cons:null_length 0 :: n__s:n__from:n__nil:0:n__cons:null_length n__cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length length1 :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length activate :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length nil :: n__s:n__from:n__nil:0:n__cons:null_length null_length :: n__s:n__from:n__nil:0:n__cons:null_length Rewrite Strategy: INNERMOST ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: from(X) -> cons(X, n__from(n__s(X))) [1] length(n__nil) -> 0 [1] length(n__cons(X, n__from(X'))) -> s(length1(from(activate(X')))) [2] length(n__cons(X, n__s(X''))) -> s(length1(s(activate(X'')))) [2] length(n__cons(X, n__nil)) -> s(length1(nil)) [2] length(n__cons(X, n__cons(X1', X2'))) -> s(length1(cons(activate(X1'), X2'))) [2] length(n__cons(X, Y)) -> s(length1(Y)) [2] length1(n__from(X3)) -> length(from(activate(X3))) [2] length1(n__s(X4)) -> length(s(activate(X4))) [2] length1(n__nil) -> length(nil) [2] length1(n__cons(X1'', X2'')) -> length(cons(activate(X1''), X2'')) [2] length1(X) -> length(X) [2] from(X) -> n__from(X) [1] s(X) -> n__s(X) [1] nil -> n__nil [1] cons(X1, X2) -> n__cons(X1, X2) [1] activate(n__from(n__from(X5))) -> from(from(activate(X5))) [2] activate(n__from(n__s(X6))) -> from(s(activate(X6))) [2] activate(n__from(n__nil)) -> from(nil) [2] activate(n__from(n__cons(X11, X21))) -> from(cons(activate(X11), X21)) [2] activate(n__from(X)) -> from(X) [2] activate(n__s(n__from(X7))) -> s(from(activate(X7))) [2] activate(n__s(n__s(X8))) -> s(s(activate(X8))) [2] activate(n__s(n__nil)) -> s(nil) [2] activate(n__s(n__cons(X12, X22))) -> s(cons(activate(X12), X22)) [2] activate(n__s(X)) -> s(X) [2] activate(n__nil) -> nil [1] activate(n__cons(n__from(X9), X2)) -> cons(from(activate(X9)), X2) [2] activate(n__cons(n__s(X10), X2)) -> cons(s(activate(X10)), X2) [2] activate(n__cons(n__nil, X2)) -> cons(nil, X2) [2] activate(n__cons(n__cons(X13, X23), X2)) -> cons(cons(activate(X13), X23), X2) [2] activate(n__cons(X1, X2)) -> cons(X1, X2) [2] activate(X) -> X [1] length(v0) -> null_length [0] The TRS has the following type information: from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length length :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__nil :: n__s:n__from:n__nil:0:n__cons:null_length 0 :: n__s:n__from:n__nil:0:n__cons:null_length n__cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length length1 :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length activate :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length nil :: n__s:n__from:n__nil:0:n__cons:null_length null_length :: n__s:n__from:n__nil:0:n__cons:null_length Rewrite Strategy: INNERMOST ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: n__nil => 1 0 => 0 null_length => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 2 }-> s(X) :|: z = 1 + X, X >= 0 activate(z) -{ 2 }-> s(s(activate(X8))) :|: X8 >= 0, z = 1 + (1 + X8) activate(z) -{ 2 }-> s(nil) :|: z = 1 + 1 activate(z) -{ 2 }-> s(from(activate(X7))) :|: X7 >= 0, z = 1 + (1 + X7) activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 1 }-> nil :|: z = 1 activate(z) -{ 2 }-> from(X) :|: z = 1 + X, X >= 0 activate(z) -{ 2 }-> from(s(activate(X6))) :|: X6 >= 0, z = 1 + (1 + X6) activate(z) -{ 2 }-> from(nil) :|: z = 1 + 1 activate(z) -{ 2 }-> from(from(activate(X5))) :|: X5 >= 0, z = 1 + (1 + X5) activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 2 }-> cons(X1, X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(nil, X2) :|: z = 1 + 1 + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(nil)) :|: z = 1 + X + 1, X >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 length1(z) -{ 2 }-> length(X) :|: X >= 0, z = X length1(z) -{ 2 }-> length(s(activate(X4))) :|: z = 1 + X4, X4 >= 0 length1(z) -{ 2 }-> length(nil) :|: z = 1 length1(z) -{ 2 }-> length(from(activate(X3))) :|: z = 1 + X3, X3 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (15) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X nil -{ 1 }-> 1 :|: cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 2 }-> s(s(activate(X8))) :|: X8 >= 0, z = 1 + (1 + X8) activate(z) -{ 2 }-> s(from(activate(X7))) :|: X7 >= 0, z = 1 + (1 + X7) activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(X6))) :|: X6 >= 0, z = 1 + (1 + X6) activate(z) -{ 2 }-> from(from(activate(X5))) :|: X5 >= 0, z = 1 + (1 + X5) activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z = 1 + X, X >= 0, X' >= 0, X = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z = 1 + X, X >= 0, X' >= 0, X = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z = 1 + 1 + X2, X2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, X2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X from(z) -{ 2 }-> 1 + X1 + X2 :|: X >= 0, z = X, X1 >= 0, X2 >= 0, X = X1, 1 + (1 + X) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z = 1 + X + 1, X >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 length1(z) -{ 2 }-> length(X) :|: X >= 0, z = X length1(z) -{ 2 }-> length(s(activate(X4))) :|: z = 1 + X4, X4 >= 0 length1(z) -{ 2 }-> length(from(activate(X3))) :|: z = 1 + X3, X3 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 ---------------------------------------- (19) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { nil } { from } { cons } { s } { activate } { length1, length } ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {nil}, {from}, {cons}, {s}, {activate}, {length1,length} ---------------------------------------- (21) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {nil}, {from}, {cons}, {s}, {activate}, {length1,length} ---------------------------------------- (23) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: nil after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (24) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {nil}, {from}, {cons}, {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: ?, size: O(1) [1] ---------------------------------------- (25) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: nil after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {from}, {cons}, {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] ---------------------------------------- (27) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {from}, {cons}, {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] ---------------------------------------- (29) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: from after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 3 + 2*z ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {from}, {cons}, {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: ?, size: O(n^1) [3 + 2*z] ---------------------------------------- (31) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: from after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {cons}, {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] ---------------------------------------- (33) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {cons}, {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] ---------------------------------------- (35) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: cons after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 1 + z + z' ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {cons}, {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: ?, size: O(n^1) [1 + z + z'] ---------------------------------------- (37) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: cons after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 4 }-> cons(X, 1 + (1 + X)) :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> cons(X', 1 + (1 + X')) :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] ---------------------------------------- (39) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] ---------------------------------------- (41) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: s after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 1 + z ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {s}, {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] s: runtime: ?, size: O(n^1) [1 + z] ---------------------------------------- (43) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: s after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 3 }-> s(1) :|: z = 1 + 1 activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] s: runtime: O(1) [1], size: O(n^1) [1 + z] ---------------------------------------- (45) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] s: runtime: O(1) [1], size: O(n^1) [1 + z] ---------------------------------------- (47) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: activate after applying outer abstraction to obtain an ITS, resulting in: EXP with polynomial bound: ? ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {activate}, {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] s: runtime: O(1) [1], size: O(n^1) [1 + z] activate: runtime: ?, size: EXP ---------------------------------------- (49) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using KoAT for: activate after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 30 + 37*z ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> s(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> s(cons(activate(X12), X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 2 }-> from(s(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(from(activate(z - 2))) :|: z - 2 >= 0 activate(z) -{ 2 }-> from(cons(activate(X11), X21)) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 2 }-> cons(s(activate(X10)), X2) :|: X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(from(activate(X9)), X2) :|: X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ 2 }-> cons(cons(activate(X13), X23), X2) :|: z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 2 }-> s(length1(s(activate(X'')))) :|: z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 2 }-> s(length1(from(activate(X')))) :|: z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 2 }-> s(length1(cons(activate(X1'), X2'))) :|: X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 2 }-> length(s(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(from(activate(z - 1))) :|: z - 1 >= 0 length1(z) -{ 2 }-> length(cons(activate(X1''), X2'')) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] s: runtime: O(1) [1], size: O(n^1) [1 + z] activate: runtime: O(n^1) [30 + 37*z], size: EXP ---------------------------------------- (51) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (52) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1 activate(z) -{ 34 + 37*X13 }-> s12 :|: s10 >= 0, s10 <= inf2, s11 >= 0, s11 <= s10 + X23 + 1, s12 >= 0, s12 <= s11 + X2 + 1, z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 34 + 37*X12 }-> s17 :|: s15 >= 0, s15 <= inf4, s16 >= 0, s16 <= s15 + X22 + 1, s17 >= 0, s17 <= s16 + 1, X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 34 + 37*X10 }-> s20 :|: s18 >= 0, s18 <= inf5, s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + X2 + 1, X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ -38 + 37*z }-> s25 :|: s23 >= 0, s23 <= inf7, s24 >= 0, s24 <= 2 * s23 + 3, s25 >= 0, s25 <= 2 * s24 + 3, z - 2 >= 0 activate(z) -{ -39 + 37*z }-> s30 :|: s28 >= 0, s28 <= inf9, s29 >= 0, s29 <= s28 + 1, s30 >= 0, s30 <= 2 * s29 + 3, z - 2 >= 0 activate(z) -{ -39 + 37*z }-> s33 :|: s31 >= 0, s31 <= inf10, s32 >= 0, s32 <= 2 * s31 + 3, s33 >= 0, s33 <= s32 + 1, z - 2 >= 0 activate(z) -{ 35 + 37*X11 }-> s36 :|: s34 >= 0, s34 <= inf11, s35 >= 0, s35 <= s34 + X21 + 1, s36 >= 0, s36 <= 2 * s35 + 3, z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 35 + 37*X9 }-> s39 :|: s37 >= 0, s37 <= inf12, s38 >= 0, s38 <= 2 * s37 + 3, s39 >= 0, s39 <= s38 + X2 + 1, X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ -40 + 37*z }-> s7 :|: s5 >= 0, s5 <= inf'', s6 >= 0, s6 <= s5 + 1, s7 >= 0, s7 <= s6 + 1, z - 2 >= 0 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 33 + 37*X1' }-> s(length1(s14)) :|: s13 >= 0, s13 <= inf3, s14 >= 0, s14 <= s13 + X2' + 1, X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 33 + 37*X'' }-> s(length1(s2)) :|: s1 >= 0, s1 <= inf, s2 >= 0, s2 <= s1 + 1, z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 34 + 37*X' }-> s(length1(s27)) :|: s26 >= 0, s26 <= inf8, s27 >= 0, s27 <= 2 * s26 + 3, z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ -3 + 37*z }-> length(s22) :|: s21 >= 0, s21 <= inf6, s22 >= 0, s22 <= 2 * s21 + 3, z - 1 >= 0 length1(z) -{ -4 + 37*z }-> length(s4) :|: s3 >= 0, s3 <= inf', s4 >= 0, s4 <= s3 + 1, z - 1 >= 0 length1(z) -{ 33 + 37*X1'' }-> length(s9) :|: s8 >= 0, s8 <= inf1, s9 >= 0, s9 <= s8 + X2'' + 1, X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] s: runtime: O(1) [1], size: O(n^1) [1 + z] activate: runtime: O(n^1) [30 + 37*z], size: EXP ---------------------------------------- (53) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: length1 after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? Computed SIZE bound using CoFloCo for: length after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1 activate(z) -{ 34 + 37*X13 }-> s12 :|: s10 >= 0, s10 <= inf2, s11 >= 0, s11 <= s10 + X23 + 1, s12 >= 0, s12 <= s11 + X2 + 1, z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 34 + 37*X12 }-> s17 :|: s15 >= 0, s15 <= inf4, s16 >= 0, s16 <= s15 + X22 + 1, s17 >= 0, s17 <= s16 + 1, X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 34 + 37*X10 }-> s20 :|: s18 >= 0, s18 <= inf5, s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + X2 + 1, X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ -38 + 37*z }-> s25 :|: s23 >= 0, s23 <= inf7, s24 >= 0, s24 <= 2 * s23 + 3, s25 >= 0, s25 <= 2 * s24 + 3, z - 2 >= 0 activate(z) -{ -39 + 37*z }-> s30 :|: s28 >= 0, s28 <= inf9, s29 >= 0, s29 <= s28 + 1, s30 >= 0, s30 <= 2 * s29 + 3, z - 2 >= 0 activate(z) -{ -39 + 37*z }-> s33 :|: s31 >= 0, s31 <= inf10, s32 >= 0, s32 <= 2 * s31 + 3, s33 >= 0, s33 <= s32 + 1, z - 2 >= 0 activate(z) -{ 35 + 37*X11 }-> s36 :|: s34 >= 0, s34 <= inf11, s35 >= 0, s35 <= s34 + X21 + 1, s36 >= 0, s36 <= 2 * s35 + 3, z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 35 + 37*X9 }-> s39 :|: s37 >= 0, s37 <= inf12, s38 >= 0, s38 <= 2 * s37 + 3, s39 >= 0, s39 <= s38 + X2 + 1, X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ -40 + 37*z }-> s7 :|: s5 >= 0, s5 <= inf'', s6 >= 0, s6 <= s5 + 1, s7 >= 0, s7 <= s6 + 1, z - 2 >= 0 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 33 + 37*X1' }-> s(length1(s14)) :|: s13 >= 0, s13 <= inf3, s14 >= 0, s14 <= s13 + X2' + 1, X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 33 + 37*X'' }-> s(length1(s2)) :|: s1 >= 0, s1 <= inf, s2 >= 0, s2 <= s1 + 1, z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 34 + 37*X' }-> s(length1(s27)) :|: s26 >= 0, s26 <= inf8, s27 >= 0, s27 <= 2 * s26 + 3, z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ -3 + 37*z }-> length(s22) :|: s21 >= 0, s21 <= inf6, s22 >= 0, s22 <= 2 * s21 + 3, z - 1 >= 0 length1(z) -{ -4 + 37*z }-> length(s4) :|: s3 >= 0, s3 <= inf', s4 >= 0, s4 <= s3 + 1, z - 1 >= 0 length1(z) -{ 33 + 37*X1'' }-> length(s9) :|: s8 >= 0, s8 <= inf1, s9 >= 0, s9 <= s8 + X2'' + 1, X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] s: runtime: O(1) [1], size: O(n^1) [1 + z] activate: runtime: O(n^1) [30 + 37*z], size: EXP length1: runtime: ?, size: INF length: runtime: ?, size: INF ---------------------------------------- (55) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: length1 after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 4 }-> s :|: s >= 0, s <= X' + (1 + (1 + X')) + 1, z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 5 }-> s' :|: s' >= 0, s' <= X + (1 + (1 + X)) + 1, z = 1 + 1, X >= 0, 1 = X activate(z) -{ 4 }-> s'' :|: s'' >= 0, s'' <= 1 + 1, z = 1 + 1 activate(z) -{ 34 + 37*X13 }-> s12 :|: s10 >= 0, s10 <= inf2, s11 >= 0, s11 <= s10 + X23 + 1, s12 >= 0, s12 <= s11 + X2 + 1, z = 1 + (1 + X13 + X23) + X2, X2 >= 0, X13 >= 0, X23 >= 0 activate(z) -{ 34 + 37*X12 }-> s17 :|: s15 >= 0, s15 <= inf4, s16 >= 0, s16 <= s15 + X22 + 1, s17 >= 0, s17 <= s16 + 1, X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) activate(z) -{ 34 + 37*X10 }-> s20 :|: s18 >= 0, s18 <= inf5, s19 >= 0, s19 <= s18 + 1, s20 >= 0, s20 <= s19 + X2 + 1, X10 >= 0, z = 1 + (1 + X10) + X2, X2 >= 0 activate(z) -{ -38 + 37*z }-> s25 :|: s23 >= 0, s23 <= inf7, s24 >= 0, s24 <= 2 * s23 + 3, s25 >= 0, s25 <= 2 * s24 + 3, z - 2 >= 0 activate(z) -{ -39 + 37*z }-> s30 :|: s28 >= 0, s28 <= inf9, s29 >= 0, s29 <= s28 + 1, s30 >= 0, s30 <= 2 * s29 + 3, z - 2 >= 0 activate(z) -{ -39 + 37*z }-> s33 :|: s31 >= 0, s31 <= inf10, s32 >= 0, s32 <= 2 * s31 + 3, s33 >= 0, s33 <= s32 + 1, z - 2 >= 0 activate(z) -{ 35 + 37*X11 }-> s36 :|: s34 >= 0, s34 <= inf11, s35 >= 0, s35 <= s34 + X21 + 1, s36 >= 0, s36 <= 2 * s35 + 3, z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 activate(z) -{ 35 + 37*X9 }-> s39 :|: s37 >= 0, s37 <= inf12, s38 >= 0, s38 <= 2 * s37 + 3, s39 >= 0, s39 <= s38 + X2 + 1, X9 >= 0, z = 1 + (1 + X9) + X2, X2 >= 0 activate(z) -{ -40 + 37*z }-> s7 :|: s5 >= 0, s5 <= inf'', s6 >= 0, s6 <= s5 + 1, s7 >= 0, s7 <= s6 + 1, z - 2 >= 0 activate(z) -{ 1 }-> z :|: z >= 0 activate(z) -{ 2 }-> 1 :|: z = 1 activate(z) -{ 4 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X activate(z) -{ 3 }-> 1 + X' :|: z - 1 >= 0, X' >= 0, z - 1 = X' activate(z) -{ 4 }-> 1 + X1 + X2' :|: z - 2 >= 0, X1 >= 0, X2' >= 0, 1 = X1, z - 2 = X2' activate(z) -{ 3 }-> 1 + X1' + X2' :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2, X1' >= 0, X2' >= 0, X1 = X1', X2 = X2' cons(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 from(z) -{ 1 }-> 1 + z :|: z >= 0 from(z) -{ 2 }-> 1 + z + X2 :|: z >= 0, X2 >= 0, 1 + (1 + z) = X2 length(z) -{ 2 }-> s(length1(Y)) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 33 + 37*X1' }-> s(length1(s14)) :|: s13 >= 0, s13 <= inf3, s14 >= 0, s14 <= s13 + X2' + 1, X2' >= 0, X1' >= 0, X >= 0, z = 1 + X + (1 + X1' + X2') length(z) -{ 33 + 37*X'' }-> s(length1(s2)) :|: s1 >= 0, s1 <= inf, s2 >= 0, s2 <= s1 + 1, z = 1 + X + (1 + X''), X >= 0, X'' >= 0 length(z) -{ 34 + 37*X' }-> s(length1(s27)) :|: s26 >= 0, s26 <= inf8, s27 >= 0, s27 <= 2 * s26 + 3, z = 1 + X + (1 + X'), X >= 0, X' >= 0 length(z) -{ 3 }-> s(length1(1)) :|: z - 2 >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: z >= 0 length1(z) -{ -3 + 37*z }-> length(s22) :|: s21 >= 0, s21 <= inf6, s22 >= 0, s22 <= 2 * s21 + 3, z - 1 >= 0 length1(z) -{ -4 + 37*z }-> length(s4) :|: s3 >= 0, s3 <= inf', s4 >= 0, s4 <= s3 + 1, z - 1 >= 0 length1(z) -{ 33 + 37*X1'' }-> length(s9) :|: s8 >= 0, s8 <= inf1, s9 >= 0, s9 <= s8 + X2'' + 1, X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 length1(z) -{ 2 }-> length(z) :|: z >= 0 length1(z) -{ 3 }-> length(1) :|: z = 1 nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + z :|: z >= 0 Function symbols to be analyzed: {length1,length} Previous analysis results are: nil: runtime: O(1) [1], size: O(1) [1] from: runtime: O(1) [2], size: O(n^1) [3 + 2*z] cons: runtime: O(1) [1], size: O(n^1) [1 + z + z'] s: runtime: O(1) [1], size: O(n^1) [1 + z] activate: runtime: O(n^1) [30 + 37*z], size: EXP length1: runtime: INF, size: INF length: runtime: ?, size: INF ---------------------------------------- (57) 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: length(v0) -> null_length [0] And the following fresh constants: null_length ---------------------------------------- (58) 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: from(X) -> cons(X, n__from(n__s(X))) [1] length(n__nil) -> 0 [1] length(n__cons(X, Y)) -> s(length1(activate(Y))) [1] length1(X) -> length(activate(X)) [1] from(X) -> n__from(X) [1] s(X) -> n__s(X) [1] nil -> n__nil [1] cons(X1, X2) -> n__cons(X1, X2) [1] activate(n__from(X)) -> from(activate(X)) [1] activate(n__s(X)) -> s(activate(X)) [1] activate(n__nil) -> nil [1] activate(n__cons(X1, X2)) -> cons(activate(X1), X2) [1] activate(X) -> X [1] length(v0) -> null_length [0] The TRS has the following type information: from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__from :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length length :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length n__nil :: n__s:n__from:n__nil:0:n__cons:null_length 0 :: n__s:n__from:n__nil:0:n__cons:null_length n__cons :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length s :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length length1 :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length activate :: n__s:n__from:n__nil:0:n__cons:null_length -> n__s:n__from:n__nil:0:n__cons:null_length nil :: n__s:n__from:n__nil:0:n__cons:null_length null_length :: n__s:n__from:n__nil:0:n__cons:null_length Rewrite Strategy: INNERMOST ---------------------------------------- (59) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: n__nil => 1 0 => 0 null_length => 0 ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: activate(z) -{ 1 }-> X :|: X >= 0, z = X activate(z) -{ 1 }-> s(activate(X)) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> nil :|: z = 1 activate(z) -{ 1 }-> from(activate(X)) :|: z = 1 + X, X >= 0 activate(z) -{ 1 }-> cons(activate(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 cons(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 from(z) -{ 1 }-> cons(X, 1 + (1 + X)) :|: X >= 0, z = X from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X length(z) -{ 1 }-> s(length1(activate(Y))) :|: Y >= 0, z = 1 + X + Y, X >= 0 length(z) -{ 1 }-> 0 :|: z = 1 length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 length1(z) -{ 1 }-> length(activate(X)) :|: X >= 0, z = X nil -{ 1 }-> 1 :|: s(z) -{ 1 }-> 1 + X :|: X >= 0, z = X Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (61) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) length(n__nil) -> 0 length(n__cons(z0, z1)) -> s(length1(activate(z1))) length1(z0) -> length(activate(z0)) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 Tuples: FROM(z0) -> c(CONS(z0, n__from(n__s(z0)))) FROM(z0) -> c1 LENGTH(n__nil) -> c2 LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1)) LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) S(z0) -> c5 NIL -> c6 CONS(z0, z1) -> c7 ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__nil) -> c10(NIL) ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0)) ACTIVATE(z0) -> c12 S tuples: FROM(z0) -> c(CONS(z0, n__from(n__s(z0)))) FROM(z0) -> c1 LENGTH(n__nil) -> c2 LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1)) LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) S(z0) -> c5 NIL -> c6 CONS(z0, z1) -> c7 ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__nil) -> c10(NIL) ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0)) ACTIVATE(z0) -> c12 K tuples:none Defined Rule Symbols: from_1, length_1, length1_1, s_1, nil, cons_2, activate_1 Defined Pair Symbols: FROM_1, LENGTH_1, LENGTH1_1, S_1, NIL, CONS_2, ACTIVATE_1 Compound Symbols: c_1, c1, c2, c3_3, c4_2, c5, c6, c7, c8_2, c9_2, c10_1, c11_2, c12 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing nodes: NIL -> c6 S(z0) -> c5 ACTIVATE(n__nil) -> c10(NIL) LENGTH(n__nil) -> c2 CONS(z0, z1) -> c7 FROM(z0) -> c1 ACTIVATE(z0) -> c12 FROM(z0) -> c(CONS(z0, n__from(n__s(z0)))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) length(n__nil) -> 0 length(n__cons(z0, z1)) -> s(length1(activate(z1))) length1(z0) -> length(activate(z0)) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 Tuples: LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1)) LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0)) S tuples: LENGTH(n__cons(z0, z1)) -> c3(S(length1(activate(z1))), LENGTH1(activate(z1)), ACTIVATE(z1)) LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__from(z0)) -> c8(FROM(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(S(activate(z0)), ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(CONS(activate(z0), z1), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: from_1, length_1, length1_1, s_1, nil, cons_2, activate_1 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_3, c4_2, c8_2, c9_2, c11_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) length(n__nil) -> 0 length(n__cons(z0, z1)) -> s(length1(activate(z1))) length1(z0) -> length(activate(z0)) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 Tuples: LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) S tuples: LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) K tuples:none Defined Rule Symbols: from_1, length_1, length1_1, s_1, nil, cons_2, activate_1 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c8_1, c9_1, c11_1 ---------------------------------------- (67) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: length(n__nil) -> 0 length(n__cons(z0, z1)) -> s(length1(activate(z1))) length1(z0) -> length(activate(z0)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) S tuples: LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c8_1, c9_1, c11_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH1(z0) -> c4(LENGTH(activate(z0)), ACTIVATE(z0)) by LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__nil) -> c4(LENGTH(nil), ACTIVATE(n__nil)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__nil) -> c4(LENGTH(nil), ACTIVATE(n__nil)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) S tuples: LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__nil) -> c4(LENGTH(nil), ACTIVATE(n__nil)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, ACTIVATE_1, LENGTH1_1 Compound Symbols: c3_2, c8_1, c9_1, c11_1, c4_2 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) S tuples: LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) K tuples:none Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, ACTIVATE_1, LENGTH1_1 Compound Symbols: c3_2, c8_1, c9_1, c11_1, c4_2, c4_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH(n__cons(z0, z1)) -> c3(LENGTH1(activate(z1)), ACTIVATE(z1)) by LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil), ACTIVATE(n__nil)) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil), ACTIVATE(n__nil)) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil), ACTIVATE(n__nil)) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) K tuples:none Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) K tuples:none Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH1(n__from(z0)) -> c4(LENGTH(from(activate(z0))), ACTIVATE(n__from(z0))) by LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(x0)) -> c4(LENGTH(n__from(activate(x0))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(x0)) -> c4(LENGTH(n__from(activate(x0))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(x0)) -> c4(LENGTH(n__from(activate(x0))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) K tuples:none Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) K tuples:none Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1 ---------------------------------------- (81) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) We considered the (Usable) Rules:none And the Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) The order we found is given by the following interpretation: Polynomial interpretation : POL(ACTIVATE(x_1)) = 0 POL(LENGTH(x_1)) = [1] POL(LENGTH1(x_1)) = [1] POL(activate(x_1)) = 0 POL(c11(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(cons(x_1, x_2)) = 0 POL(from(x_1)) = 0 POL(n__cons(x_1, x_2)) = x_1 POL(n__from(x_1)) = 0 POL(n__nil) = 0 POL(n__s(x_1)) = 0 POL(nil) = 0 POL(s(x_1)) = 0 ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH1(n__s(z0)) -> c4(LENGTH(s(activate(z0))), ACTIVATE(n__s(z0))) by LENGTH1(n__s(x0)) -> c4(LENGTH(n__s(activate(x0))), ACTIVATE(n__s(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(LENGTH(n__s(activate(x0))), ACTIVATE(n__s(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(x0)) -> c4(LENGTH(n__s(activate(x0))), ACTIVATE(n__s(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1 ---------------------------------------- (87) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) We considered the (Usable) Rules:none And the Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) The order we found is given by the following interpretation: Polynomial interpretation : POL(ACTIVATE(x_1)) = 0 POL(LENGTH(x_1)) = [1] POL(LENGTH1(x_1)) = [1] POL(activate(x_1)) = 0 POL(c11(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(cons(x_1, x_2)) = 0 POL(from(x_1)) = 0 POL(n__cons(x_1, x_2)) = x_1 POL(n__from(x_1)) = 0 POL(n__nil) = 0 POL(n__s(x_1)) = 0 POL(nil) = 0 POL(s(x_1)) = 0 ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) by LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH1(n__nil) -> c4(LENGTH(nil)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c4_1, c3_2, c3_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH1(n__nil) -> c4(LENGTH(nil)) by LENGTH1(n__nil) -> c4(LENGTH(n__nil)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH1(n__nil) -> c4(LENGTH(n__nil)) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH1(n__nil) -> c4(LENGTH(n__nil)) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: LENGTH1(n__nil) -> c4(LENGTH(n__nil)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(activate(z0))), ACTIVATE(n__from(z0))) by LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(activate(z0))), ACTIVATE(n__s(z0))) by LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH(n__cons(x0, n__cons(z0, z1))) -> c3(LENGTH1(cons(activate(z0), z1)), ACTIVATE(n__cons(z0, z1))) by LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c3_1, c4_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(nil)) by LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH1(n__s(z0)) -> c4(LENGTH(s(z0)), ACTIVATE(n__s(z0))) by LENGTH1(n__s(z0)) -> c4(LENGTH(n__s(z0)), ACTIVATE(n__s(z0))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__s(z0)) -> c4(LENGTH(n__s(z0)), ACTIVATE(n__s(z0))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__s(z0)) -> c4(LENGTH(n__s(z0)), ACTIVATE(n__s(z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__s(z0)) -> c4(ACTIVATE(n__s(z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1 ---------------------------------------- (107) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__s(z0)) -> c4(ACTIVATE(n__s(z0))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1 ---------------------------------------- (109) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(nil)), ACTIVATE(n__from(n__nil))) by LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1 ---------------------------------------- (111) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH1(n__s(n__nil)) -> c4(LENGTH(s(nil)), ACTIVATE(n__s(n__nil))) by LENGTH1(n__s(n__nil)) -> c4(LENGTH(n__s(nil)), ACTIVATE(n__s(n__nil))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(n__s(nil)), ACTIVATE(n__s(n__nil))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__s(n__nil)) -> c4(LENGTH(n__s(nil)), ACTIVATE(n__s(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1 ---------------------------------------- (115) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) We considered the (Usable) Rules:none And the Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) The order we found is given by the following interpretation: Polynomial interpretation : POL(ACTIVATE(x_1)) = 0 POL(LENGTH(x_1)) = [1] POL(LENGTH1(x_1)) = [1] POL(activate(x_1)) = 0 POL(c11(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(cons(x_1, x_2)) = 0 POL(from(x_1)) = 0 POL(n__cons(x_1, x_2)) = 0 POL(n__from(x_1)) = 0 POL(n__nil) = 0 POL(n__s(x_1)) = 0 POL(nil) = 0 POL(s(x_1)) = 0 ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) S tuples: ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c8_1, c9_1, c11_1, c4_2, c3_2, c4_1, c3_1 ---------------------------------------- (117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__from(z0)) -> c8(ACTIVATE(z0)) by ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) S tuples: ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil)), ACTIVATE(n__from(n__nil))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c9_1, c11_1, c4_2, c3_2, c4_1, c3_1, c8_1 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) S tuples: ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c9_1, c11_1, c4_2, c3_2, c4_1, c3_1, c8_1 ---------------------------------------- (121) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__s(z0)) -> c9(ACTIVATE(z0)) by ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) S tuples: ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c11_1, c4_2, c3_2, c4_1, c3_1, c8_1, c9_1 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: LENGTH1(n__s(n__nil)) -> c4(ACTIVATE(n__s(n__nil))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) S tuples: ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil)), ACTIVATE(n__s(n__nil))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c11_1, c4_2, c3_2, c4_1, c3_1, c8_1, c9_1 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) S tuples: ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: ACTIVATE_1, LENGTH1_1, LENGTH_1 Compound Symbols: c11_1, c4_2, c3_2, c4_1, c3_1, c8_1, c9_1 ---------------------------------------- (127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__cons(z0, z1)) -> c11(ACTIVATE(z0)) by ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) S tuples: LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1)), ACTIVATE(n__cons(n__nil, x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2)), ACTIVATE(n__cons(n__nil, x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c3_1, c8_1, c9_1, c11_1 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) S tuples: LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c3_1, c8_1, c9_1, c11_1 ---------------------------------------- (131) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH1(n__cons(z0, x1)) -> c4(LENGTH(cons(z0, x1)), ACTIVATE(n__cons(z0, x1))) by LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) S tuples: LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c3_1, c8_1, c9_1, c11_1 ---------------------------------------- (133) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace LENGTH1(z0) -> c4(LENGTH(z0), ACTIVATE(z0)) by LENGTH1(n__cons(y0, y1)) -> c4(LENGTH(n__cons(y0, y1)), ACTIVATE(n__cons(y0, y1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c3_1, c8_1, c9_1, c11_1 ---------------------------------------- (135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: LENGTH(n__cons(x0, n__nil)) -> c3(LENGTH1(n__nil)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__from(n__from(y0))) -> c4(LENGTH(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(LENGTH(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(LENGTH(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__s(n__s(y0))) -> c4(LENGTH(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(LENGTH(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(LENGTH(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(LENGTH(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(LENGTH(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1 ---------------------------------------- (139) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) We considered the (Usable) Rules:none And the Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) The order we found is given by the following interpretation: Polynomial interpretation : POL(ACTIVATE(x_1)) = 0 POL(LENGTH(x_1)) = [1] POL(LENGTH1(x_1)) = [1] POL(activate(x_1)) = 0 POL(c11(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(cons(x_1, x_2)) = 0 POL(from(x_1)) = 0 POL(n__cons(x_1, x_2)) = 0 POL(n__from(x_1)) = 0 POL(n__nil) = 0 POL(n__s(x_1)) = 0 POL(nil) = 0 POL(s(x_1)) = 0 ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1 ---------------------------------------- (141) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) We considered the (Usable) Rules: from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) cons(z0, z1) -> n__cons(z0, z1) And the Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) The order we found is given by the following interpretation: Polynomial interpretation : POL(ACTIVATE(x_1)) = 0 POL(LENGTH(x_1)) = x_1 POL(LENGTH1(x_1)) = [1] POL(activate(x_1)) = 0 POL(c11(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(cons(x_1, x_2)) = [1] POL(from(x_1)) = [1] POL(n__cons(x_1, x_2)) = [1] POL(n__from(x_1)) = 0 POL(n__nil) = 0 POL(n__s(x_1)) = 0 POL(nil) = 0 POL(s(x_1)) = 0 ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1 ---------------------------------------- (143) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH(n__cons(x0, n__s(z0))) -> c3(LENGTH1(s(z0)), ACTIVATE(n__s(z0))) by LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1 ---------------------------------------- (145) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH(n__cons(x0, n__cons(z0, x2))) -> c3(LENGTH1(cons(z0, x2)), ACTIVATE(n__cons(z0, x2))) by LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c3_1, c9_1, c11_1 ---------------------------------------- (147) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH(n__cons(x0, n__from(n__nil))) -> c3(LENGTH1(from(nil))) by LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c9_1, c3_1, c11_1 ---------------------------------------- (149) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(s(nil))) by LENGTH(n__cons(z0, n__s(n__nil))) -> c3(LENGTH1(n__s(nil))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(z0, n__s(n__nil))) -> c3(LENGTH1(n__s(nil))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(z0, n__s(n__nil))) -> c3(LENGTH1(n__s(nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace LENGTH(n__cons(z0, n__s(n__nil))) -> c3(LENGTH1(n__s(nil))) by LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (153) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH1(n__cons(n__nil, x1)) -> c4(LENGTH(cons(nil, x1))) by LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (155) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH(n__cons(x0, n__cons(n__nil, x2))) -> c3(LENGTH1(cons(nil, x2))) by LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (157) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(nil, z0))) by LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (159) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(nil, z1))) by LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) S tuples: LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH_1, LENGTH1_1, ACTIVATE_1 Compound Symbols: c3_2, c4_2, c4_1, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (161) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace LENGTH(n__cons(x0, z0)) -> c3(LENGTH1(z0), ACTIVATE(z0)) by LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(y0))) -> c3(LENGTH1(n__s(y0)), ACTIVATE(n__s(y0))) LENGTH(n__cons(z0, n__cons(y0, y1))) -> c3(LENGTH1(n__cons(y0, y1)), ACTIVATE(n__cons(y0, y1))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(n__nil, y0))) -> c3(LENGTH1(n__cons(n__nil, y0)), ACTIVATE(n__cons(n__nil, y0))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(n__nil, y0))) -> c3(LENGTH1(n__cons(n__nil, y0)), ACTIVATE(n__cons(n__nil, y0))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__nil)) -> c4(LENGTH(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil)), ACTIVATE(n__from(n__nil))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(n__nil, y0))) -> c3(LENGTH1(n__cons(n__nil, y0)), ACTIVATE(n__cons(n__nil, y0))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (165) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) We considered the (Usable) Rules:none And the Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) The order we found is given by the following interpretation: Polynomial interpretation : POL(ACTIVATE(x_1)) = 0 POL(LENGTH(x_1)) = [1] POL(LENGTH1(x_1)) = [1] POL(activate(x_1)) = 0 POL(c11(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(cons(x_1, x_2)) = 0 POL(from(x_1)) = 0 POL(n__cons(x_1, x_2)) = 0 POL(n__from(x_1)) = 0 POL(n__nil) = 0 POL(n__s(x_1)) = 0 POL(nil) = [1] POL(s(x_1)) = 0 ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (167) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) We considered the (Usable) Rules: from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) cons(z0, z1) -> n__cons(z0, z1) And the Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) The order we found is given by the following interpretation: Polynomial interpretation : POL(ACTIVATE(x_1)) = 0 POL(LENGTH(x_1)) = x_1 POL(LENGTH1(x_1)) = x_1 POL(activate(x_1)) = 0 POL(c11(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c3(x_1, x_2)) = x_1 + x_2 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(cons(x_1, x_2)) = [1] POL(from(x_1)) = [1] POL(n__cons(x_1, x_2)) = [1] POL(n__from(x_1)) = [1] POL(n__nil) = 0 POL(n__s(x_1)) = 0 POL(nil) = [1] POL(s(x_1)) = 0 ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) K tuples: LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace LENGTH1(n__from(x0)) -> c4(ACTIVATE(n__from(x0))) by LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) K tuples: LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) by LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__s(x0)) -> c4(ACTIVATE(n__s(x0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c4_1, c3_2, c8_1, c9_1, c11_1, c3_1 ---------------------------------------- (173) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace LENGTH1(n__s(z0)) -> c4(ACTIVATE(n__s(z0))) by LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c8_1, c4_1, c9_1, c11_1, c3_1 ---------------------------------------- (175) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: LENGTH(n__cons(x0, n__s(n__nil))) -> c3(LENGTH1(n__s(n__nil))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c8_1, c4_1, c9_1, c11_1, c3_1 ---------------------------------------- (177) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__from(n__from(y0))) -> c8(ACTIVATE(n__from(y0))) by ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c8_1, c4_1, c9_1, c11_1, c3_1 ---------------------------------------- (179) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__from(n__s(y0))) -> c8(ACTIVATE(n__s(y0))) by ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c8_1, c4_1, c9_1, c11_1, c3_1 ---------------------------------------- (181) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__from(n__cons(y0, y1))) -> c8(ACTIVATE(n__cons(y0, y1))) by ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1 ---------------------------------------- (183) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__s(n__s(y0))) -> c9(ACTIVATE(n__s(y0))) by ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1 ---------------------------------------- (185) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__s(n__cons(y0, y1))) -> c9(ACTIVATE(n__cons(y0, y1))) by ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1 ---------------------------------------- (187) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__s(n__from(n__from(y0)))) -> c9(ACTIVATE(n__from(n__from(y0)))) by ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1 ---------------------------------------- (189) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__s(n__from(n__s(y0)))) -> c9(ACTIVATE(n__from(n__s(y0)))) by ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), 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n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c9_1, c11_1, c3_1, c8_1 ---------------------------------------- (191) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__s(n__from(n__cons(y0, y1)))) -> c9(ACTIVATE(n__from(n__cons(y0, y1)))) by ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1 ---------------------------------------- (193) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__cons(n__cons(y0, y1), z1)) -> c11(ACTIVATE(n__cons(y0, y1))) by ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> 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LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) 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c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1 ---------------------------------------- (195) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__cons(n__from(n__from(y0)), z1)) -> c11(ACTIVATE(n__from(n__from(y0)))) by ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1 ---------------------------------------- (197) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__cons(n__from(n__s(y0)), z1)) -> c11(ACTIVATE(n__from(n__s(y0)))) by ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1 ---------------------------------------- (199) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__from(n__cons(y0, y1)))) by ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) 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c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1 ---------------------------------------- (201) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__cons(n__s(n__s(y0)), z1)) -> c11(ACTIVATE(n__s(n__s(y0)))) by ACTIVATE(n__cons(n__s(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__s(n__s(y0))))) ACTIVATE(n__cons(n__s(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1)))))) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__s(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__s(n__s(y0))))) ACTIVATE(n__cons(n__s(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1)))))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__s(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__s(n__s(y0))))) ACTIVATE(n__cons(n__s(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1)))))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1 ---------------------------------------- (203) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1)) -> c11(ACTIVATE(n__s(n__cons(y0, y1)))) by ACTIVATE(n__cons(n__s(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: activate(n__from(z0)) -> from(activate(z0)) activate(n__s(z0)) -> s(activate(z0)) activate(n__nil) -> nil activate(n__cons(z0, z1)) -> cons(activate(z0), z1) activate(z0) -> z0 from(z0) -> cons(z0, n__from(n__s(z0))) from(z0) -> n__from(z0) s(z0) -> n__s(z0) nil -> n__nil cons(z0, z1) -> n__cons(z0, z1) Tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, 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y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, 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c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__s(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__s(n__s(y0))))) ACTIVATE(n__cons(n__s(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__cons(n__s(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) S tuples: LENGTH1(n__from(x0)) -> c4(LENGTH(cons(activate(x0), n__from(n__s(activate(x0))))), ACTIVATE(n__from(x0))) LENGTH1(n__from(n__from(z0))) -> c4(LENGTH(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH1(n__from(n__s(z0))) -> c4(LENGTH(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH1(n__from(n__cons(z0, z1))) -> c4(LENGTH(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH1(n__from(z0)) -> c4(LENGTH(from(z0)), ACTIVATE(n__from(z0))) LENGTH1(n__cons(x0, z1)) -> c4(LENGTH(n__cons(activate(x0), z1)), ACTIVATE(n__cons(x0, z1))) LENGTH1(n__cons(n__from(z0), x1)) -> c4(LENGTH(cons(from(activate(z0)), x1)), ACTIVATE(n__cons(n__from(z0), x1))) LENGTH1(n__cons(n__s(z0), x1)) -> c4(LENGTH(cons(s(activate(z0)), x1)), ACTIVATE(n__cons(n__s(z0), x1))) LENGTH1(n__cons(n__cons(z0, z1), x1)) -> c4(LENGTH(cons(cons(activate(z0), z1), x1)), ACTIVATE(n__cons(n__cons(z0, z1), x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(cons(activate(x1), n__from(n__s(activate(x1))))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(x1))) -> c3(LENGTH1(n__from(activate(x1))), ACTIVATE(n__from(x1))) LENGTH(n__cons(x0, n__from(n__from(z0)))) -> c3(LENGTH1(from(from(activate(z0)))), ACTIVATE(n__from(n__from(z0)))) LENGTH(n__cons(x0, n__from(n__s(z0)))) -> c3(LENGTH1(from(s(activate(z0)))), ACTIVATE(n__from(n__s(z0)))) LENGTH(n__cons(x0, n__from(n__cons(z0, z1)))) -> c3(LENGTH1(from(cons(activate(z0), z1))), ACTIVATE(n__from(n__cons(z0, z1)))) LENGTH(n__cons(x0, n__from(z0))) -> c3(LENGTH1(from(z0)), ACTIVATE(n__from(z0))) LENGTH(n__cons(x0, n__cons(x1, z1))) -> c3(LENGTH1(n__cons(activate(x1), z1)), ACTIVATE(n__cons(x1, z1))) LENGTH(n__cons(x0, n__cons(n__from(z0), x2))) -> c3(LENGTH1(cons(from(activate(z0)), x2)), ACTIVATE(n__cons(n__from(z0), x2))) LENGTH(n__cons(x0, n__cons(n__s(z0), x2))) -> c3(LENGTH1(cons(s(activate(z0)), x2)), ACTIVATE(n__cons(n__s(z0), x2))) LENGTH(n__cons(x0, n__cons(n__cons(z0, z1), x2))) -> c3(LENGTH1(cons(cons(activate(z0), z1), x2)), ACTIVATE(n__cons(n__cons(z0, z1), x2))) LENGTH1(n__from(n__nil)) -> c4(LENGTH(from(n__nil))) ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__cons(z0, z1)) -> c4(LENGTH(n__cons(z0, z1)), ACTIVATE(n__cons(z0, z1))) LENGTH1(n__cons(y0, n__from(y1))) -> c4(LENGTH(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH1(n__cons(y0, n__from(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH1(n__cons(y0, n__from(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__s(y1))) -> c4(LENGTH(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH1(n__cons(y0, n__s(n__from(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH1(n__cons(y0, n__s(n__s(y1)))) -> c4(LENGTH(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))) -> c4(LENGTH(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH1(n__cons(y0, n__cons(y1, y2))) -> c4(LENGTH(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))) -> c4(LENGTH(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))) -> c4(LENGTH(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH1(n__cons(y0, n__from(n__nil))) -> c4(LENGTH(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH1(n__cons(y0, n__s(n__nil))) -> c4(LENGTH(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH1(n__cons(n__cons(y0, y1), y2)) -> c4(LENGTH(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH1(n__cons(n__from(n__from(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH1(n__cons(n__from(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__s(y0)), y1)) -> c4(LENGTH(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)) -> c4(LENGTH(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)) -> c4(LENGTH(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)) -> c4(LENGTH(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH1(n__cons(y0, n__cons(n__nil, y1))) -> c4(LENGTH(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__cons(z1, z2))) -> c3(LENGTH1(n__cons(z1, z2)), ACTIVATE(n__cons(z1, z2))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(from(n__nil))) LENGTH1(n__cons(n__nil, z0)) -> c4(LENGTH(n__cons(n__nil, z0))) LENGTH(n__cons(z0, n__cons(n__nil, z1))) -> c3(LENGTH1(n__cons(n__nil, z1))) LENGTH(n__cons(z0, n__from(y0))) -> c3(LENGTH1(n__from(y0)), ACTIVATE(n__from(y0))) LENGTH(n__cons(z0, n__from(n__from(y0)))) -> c3(LENGTH1(n__from(n__from(y0))), ACTIVATE(n__from(n__from(y0)))) LENGTH(n__cons(z0, n__from(n__s(y0)))) -> c3(LENGTH1(n__from(n__s(y0))), ACTIVATE(n__from(n__s(y0)))) LENGTH(n__cons(z0, n__from(n__cons(y0, y1)))) -> c3(LENGTH1(n__from(n__cons(y0, y1))), ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__cons(n__from(y0), y1))) -> c3(LENGTH1(n__cons(n__from(y0), y1)), ACTIVATE(n__cons(n__from(y0), y1))) LENGTH(n__cons(z0, n__cons(n__s(y0), y1))) -> c3(LENGTH1(n__cons(n__s(y0), y1)), ACTIVATE(n__cons(n__s(y0), y1))) LENGTH(n__cons(z0, n__cons(n__cons(y0, y1), y2))) -> c3(LENGTH1(n__cons(n__cons(y0, y1), y2)), ACTIVATE(n__cons(n__cons(y0, y1), y2))) LENGTH(n__cons(z0, n__cons(n__from(n__from(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__from(y0)), y1)), ACTIVATE(n__cons(n__from(n__from(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__from(n__s(y0)), y1)), ACTIVATE(n__cons(n__from(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__from(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__from(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__from(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__s(y0)), y1))) -> c3(LENGTH1(n__cons(n__s(n__s(y0)), y1)), ACTIVATE(n__cons(n__s(n__s(y0)), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__cons(y0, y1)), y2))) -> c3(LENGTH1(n__cons(n__s(n__cons(y0, y1)), y2)), ACTIVATE(n__cons(n__s(n__cons(y0, y1)), y2))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__from(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__from(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__from(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__s(y0))), y1))) -> c3(LENGTH1(n__cons(n__s(n__from(n__s(y0))), y1)), ACTIVATE(n__cons(n__s(n__from(n__s(y0))), y1))) LENGTH(n__cons(z0, n__cons(n__s(n__from(n__cons(y0, y1))), y2))) -> c3(LENGTH1(n__cons(n__s(n__from(n__cons(y0, y1))), y2)), ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), y2))) LENGTH(n__cons(z0, n__cons(y0, n__from(y1)))) -> c3(LENGTH1(n__cons(y0, n__from(y1))), ACTIVATE(n__cons(y0, n__from(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__from(y1)))), ACTIVATE(n__cons(y0, n__from(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__from(n__s(y1)))), ACTIVATE(n__cons(y0, n__from(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__from(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__from(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__s(y1)))) -> c3(LENGTH1(n__cons(y0, n__s(y1))), ACTIVATE(n__cons(y0, n__s(y1)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__from(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__from(y1)))), ACTIVATE(n__cons(y0, n__s(n__from(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__s(y1))))) -> c3(LENGTH1(n__cons(y0, n__s(n__s(y1)))), ACTIVATE(n__cons(y0, n__s(n__s(y1))))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__cons(y1, y2))))) -> c3(LENGTH1(n__cons(y0, n__s(n__cons(y1, y2)))), ACTIVATE(n__cons(y0, n__s(n__cons(y1, y2))))) LENGTH(n__cons(z0, n__cons(y0, n__cons(y1, y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(y1, y2))), ACTIVATE(n__cons(y0, n__cons(y1, y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__from(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__from(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__from(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__s(y1), y2)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__s(y1), y2))), ACTIVATE(n__cons(y0, n__cons(n__s(y1), y2)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__cons(y1, y2), y3)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__cons(y1, y2), y3))), ACTIVATE(n__cons(y0, n__cons(n__cons(y1, y2), y3)))) LENGTH(n__cons(z0, n__cons(y0, n__nil))) -> c3(LENGTH1(n__cons(y0, n__nil)), ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(z0, n__cons(y0, n__from(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__from(n__nil))), ACTIVATE(n__cons(y0, n__from(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__s(n__nil)))) -> c3(LENGTH1(n__cons(y0, n__s(n__nil))), ACTIVATE(n__cons(y0, n__s(n__nil)))) LENGTH(n__cons(z0, n__cons(y0, n__cons(n__nil, y1)))) -> c3(LENGTH1(n__cons(y0, n__cons(n__nil, y1))), ACTIVATE(n__cons(y0, n__cons(n__nil, y1)))) LENGTH(n__cons(z0, n__from(n__nil))) -> c3(LENGTH1(n__from(n__nil))) ACTIVATE(n__from(n__from(n__from(y0)))) -> c8(ACTIVATE(n__from(n__from(y0)))) ACTIVATE(n__from(n__from(n__s(y0)))) -> c8(ACTIVATE(n__from(n__s(y0)))) ACTIVATE(n__from(n__from(n__cons(y0, y1)))) -> c8(ACTIVATE(n__from(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__s(y0)))) -> c8(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__from(n__s(n__cons(y0, y1)))) -> c8(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__from(n__s(n__from(n__from(y0))))) -> c8(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__from(n__s(n__from(n__s(y0))))) -> c8(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1))))) -> c8(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1))) -> c8(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1))) -> c8(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c8(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__s(n__s(y0)))) -> c9(ACTIVATE(n__s(n__s(y0)))) ACTIVATE(n__s(n__s(n__cons(y0, y1)))) -> c9(ACTIVATE(n__s(n__cons(y0, y1)))) ACTIVATE(n__s(n__s(n__from(n__from(y0))))) -> c9(ACTIVATE(n__s(n__from(n__from(y0))))) ACTIVATE(n__s(n__s(n__from(n__s(y0))))) -> c9(ACTIVATE(n__s(n__from(n__s(y0))))) ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1))) -> c9(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1))) -> c9(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) -> c9(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__s(n__from(n__from(n__from(y0))))) -> c9(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__s(n__from(n__from(n__s(y0))))) -> c9(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__s(n__from(n__from(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__s(y0))))) -> c9(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__s(n__from(n__s(n__cons(y0, y1))))) -> c9(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__s(n__from(n__s(n__from(n__from(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__s(y0)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__s(n__from(n__s(n__from(n__cons(y0, y1)))))) -> c9(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__s(n__from(n__cons(n__cons(y0, y1), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__from(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__s(y0)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__s(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) -> c9(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__cons(n__cons(y0, y1), z1), z2)) -> c11(ACTIVATE(n__cons(n__cons(y0, y1), z1))) ACTIVATE(n__cons(n__cons(n__from(n__from(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__from(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__from(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__from(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__s(y0)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__s(y0)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__cons(y0, y1)), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__cons(y0, y1)), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__from(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__from(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__s(y0))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__s(y0))), z1))) ACTIVATE(n__cons(n__cons(n__s(n__from(n__cons(y0, y1))), z1), z2)) -> c11(ACTIVATE(n__cons(n__s(n__from(n__cons(y0, y1))), z1))) ACTIVATE(n__cons(n__from(n__from(n__from(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__from(y0))))) ACTIVATE(n__cons(n__from(n__from(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__from(n__s(y0))))) ACTIVATE(n__cons(n__from(n__from(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__from(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__from(n__s(n__s(y0))))) ACTIVATE(n__cons(n__from(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__from(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__from(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__from(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__cons(n__from(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__from(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) ACTIVATE(n__cons(n__s(n__s(n__s(y0))), z1)) -> c11(ACTIVATE(n__s(n__s(n__s(y0))))) ACTIVATE(n__cons(n__s(n__s(n__cons(y0, y1))), z1)) -> c11(ACTIVATE(n__s(n__s(n__cons(y0, y1))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__from(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__from(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__s(y0)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__s(y0)))))) ACTIVATE(n__cons(n__s(n__s(n__from(n__cons(y0, y1)))), z1)) -> c11(ACTIVATE(n__s(n__s(n__from(n__cons(y0, y1)))))) ACTIVATE(n__cons(n__s(n__cons(n__cons(y0, y1), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__cons(y0, y1), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__from(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__from(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__s(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__from(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__from(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__s(y0)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__s(y0)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__cons(y0, y1)), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__cons(y0, y1)), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__from(y0))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__from(y0))), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__s(y0))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__s(y0))), z1)))) ACTIVATE(n__cons(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1)), z2)) -> c11(ACTIVATE(n__s(n__cons(n__s(n__from(n__cons(y0, y1))), z1)))) K tuples: LENGTH1(n__from(n__from(y0))) -> c4(ACTIVATE(n__from(n__from(y0)))) LENGTH1(n__from(n__s(y0))) -> c4(ACTIVATE(n__from(n__s(y0)))) LENGTH1(n__from(n__cons(y0, y1))) -> c4(ACTIVATE(n__from(n__cons(y0, y1)))) LENGTH1(n__s(n__s(y0))) -> c4(ACTIVATE(n__s(n__s(y0)))) LENGTH1(n__s(n__cons(y0, y1))) -> c4(ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH1(n__s(n__from(n__from(y0)))) -> c4(ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH1(n__s(n__from(n__s(y0)))) -> c4(ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH1(n__s(n__from(n__cons(y0, y1)))) -> c4(ACTIVATE(n__s(n__from(n__cons(y0, y1))))) LENGTH1(n__s(n__from(z0))) -> c4(LENGTH(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH1(n__s(n__s(z0))) -> c4(LENGTH(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH1(n__s(n__cons(z0, z1))) -> c4(LENGTH(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH1(n__cons(y0, n__nil)) -> c4(ACTIVATE(n__cons(y0, n__nil))) LENGTH(n__cons(x0, n__s(x1))) -> c3(LENGTH1(n__s(activate(x1))), ACTIVATE(n__s(x1))) LENGTH(n__cons(x0, n__s(n__from(z0)))) -> c3(LENGTH1(s(from(activate(z0)))), ACTIVATE(n__s(n__from(z0)))) LENGTH(n__cons(x0, n__s(n__s(z0)))) -> c3(LENGTH1(s(s(activate(z0)))), ACTIVATE(n__s(n__s(z0)))) LENGTH(n__cons(x0, n__s(n__cons(z0, z1)))) -> c3(LENGTH1(s(cons(activate(z0), z1))), ACTIVATE(n__s(n__cons(z0, z1)))) LENGTH(n__cons(z0, n__s(z1))) -> c3(LENGTH1(n__s(z1)), ACTIVATE(n__s(z1))) LENGTH(n__cons(z0, n__s(n__from(y0)))) -> c3(LENGTH1(n__s(n__from(y0))), ACTIVATE(n__s(n__from(y0)))) LENGTH(n__cons(z0, n__s(n__s(y0)))) -> c3(LENGTH1(n__s(n__s(y0))), ACTIVATE(n__s(n__s(y0)))) LENGTH(n__cons(z0, n__s(n__cons(y0, y1)))) -> c3(LENGTH1(n__s(n__cons(y0, y1))), ACTIVATE(n__s(n__cons(y0, y1)))) LENGTH(n__cons(z0, n__s(n__from(n__from(y0))))) -> c3(LENGTH1(n__s(n__from(n__from(y0)))), ACTIVATE(n__s(n__from(n__from(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__s(y0))))) -> c3(LENGTH1(n__s(n__from(n__s(y0)))), ACTIVATE(n__s(n__from(n__s(y0))))) LENGTH(n__cons(z0, n__s(n__from(n__cons(y0, y1))))) -> c3(LENGTH1(n__s(n__from(n__cons(y0, y1)))), ACTIVATE(n__s(n__from(n__cons(y0, y1))))) Defined Rule Symbols: activate_1, from_1, s_1, nil, cons_2 Defined Pair Symbols: LENGTH1_1, LENGTH_1, ACTIVATE_1 Compound Symbols: c4_2, c3_2, c4_1, c11_1, c3_1, c8_1, c9_1